Definition 1
Classical mechanics is a subsection of physics that studies the movement of physical bodies based on Newton's laws.
The basic concepts of classical mechanics are:
- mass - is defined as the main measure of inertia, or the ability of a substance to maintain a state of rest in the absence of the influence of external factors on it;
- force - acts on the body and changes the state of its movement, causing acceleration;
- internal energy - determines the current state of the element under study.
Other equally important concepts of this section of physics are: temperature, momentum, angular momentum and volume of matter. The energy of a mechanical system mainly consists of its kinetic energy of motion and the potential force, which depends on the position of the forces acting in certain system elements. With respect to these physical quantities, the fundamental laws of conservation of classical mechanics operate.
Founders of classical mechanics
Remark 1
The foundations of classical mechanics were successfully laid by the thinker Galileo, as well as Kepler and Copernicus when considering the laws of rapid motion. celestial bodies.
Figure 1. Principles of classical mechanics. Author24 - online exchange of student papers
Interestingly, for a long period of time, physics and mechanics were studied in the context of astronomical events. In his scientific works, Copernicus argued that the correct calculation of the patterns of interaction of celestial bodies can be simplified if we deviate from the existing principles that were previously laid down by Aristotle and consider it the starting point for the transition from the geocentric to the heliocentric concept.
The ideas of the scientist were further formalized by his colleague Kepler in the three laws of motion of material bodies. In particular, the second law stated that absolutely all the planets of the solar system carry out uniform movement in elliptical orbits, with the main focus of the Sun.
The next significant contribution to the development of classical mechanics was made by the inventor Galileo, who, studying the fundamental postulates of the mechanical motion of celestial bodies, in particular under the influence of the forces of gravity, presented the public with five universal laws of the physical motion of substances at once.
But still, contemporaries attribute the laurels of the key founder of classical mechanics to Isaac Newton, who in his famous scientific work « mathematical expression natural philosophy" described the synthesis of those definitions of the physics of motion, which were previously presented by his predecessors.
Figure 2. Variational principles of classical mechanics. Author24 - online exchange of student papers
Newton clearly formulated the three basic laws of motion, which were named after him, as well as the theory of universal gravitation, which drew a line under Galileo's research and explained the phenomenon of free fall of bodies. Thus, a new, more improved picture of the world was developed.
Basic and variational principles of classical mechanics
Classical mechanics provides researchers with accurate results for systems that are often found in Everyday life. But they eventually become incorrect for other concepts, the speed of which is almost equal to the speed of light. Then in experiments it is necessary to use the laws of relativistic and quantum mechanics. For systems that combine several properties at once, instead of classical mechanics, the theory of the field of quanta is used. For concepts with many components, or levels of freedom, the direction of study in physics is also adequate when using the methods of statistical mechanics.
Today, the following main principles of classical mechanics are distinguished:
- The principle of invariance with respect to spatial and temporal displacements (rotations, shifts, symmetries): space is always homogeneous, and the course of any processes within a closed system is not affected by its initial locations and orientation relative to the material reference body.
- The principle of relativity: the flow of physical processes in an isolated system is not affected by its rectilinear motion relative to the very concept of reference; the laws that describe such phenomena are the same in different branches of physics; the processes themselves will be the same if the initial conditions were identical.
Definition 2
Variational principles are the initial, basic provisions of analytical mechanics, mathematically expressed in the form of unique variational relations, from which differential formulas of motion follow as a logical consequence, as well as all kinds of provisions and laws of classical mechanics.
In most cases, the main feature by which the real motion can be distinguished from the considered class of kinematic motions is the stationarity condition, which ensures the invariance of the further description.
Figure 4. The principle of long-range action. Author24 - online exchange of student papers
The first of the variational rules of classical mechanics is the principle of possible or virtual displacements, which allows you to find the correct equilibrium positions of the system material points. Therefore, this pattern helps to solve challenging tasks statics.
The next principle is called the least constraint. This postulate presupposes a certain movement of a system of material points, directly interconnected in a chaotic way and subject to any influences from the environment.
Another major variational proposition in classical mechanics is the principle of the straightest path, where any free system is in a state of rest or uniform motion along specific lines compared to any other arcs allowed by relationships and having a common starting point and tangent in concept.
Operating principle in classical mechanics
Newton's equations of mechanical motion can be formulated in many ways. One is through the Lagrange formalism, also called Lagrangian mechanics. Although this principle is quite equivalent to Newton's laws in classical physics, but the interpretation of action is better suited for generalizations of all concepts and plays important role V modern science. Indeed, this principle is a complex generalization in physics.
In particular, this is fully understood within the framework of quantum mechanics. The interpretation of quantum mechanics by Richard Feynman through the use of path integrals is based on the principle of constant interaction.
Many problems in physics can be solved by applying the principle of operation, which is able to find the fastest and easiest way to solve the problems.
For example, light can find its way through optical system, and the trajectory of a material body in a gravitational field can be detected using the same operating principle.
Symmetries in any situation can be better understood by applying this concept, together with the Euler-Lagrange equations. In classical mechanics right choice further action can be experimentally proved from Newton's laws of motion. And, conversely, from the principle of action, Newtonian equations are implemented in practice, with a competent choice of action.
Thus, in classical mechanics, the principle of action is considered ideally equivalent to Newton's equations of motion. The application of this method greatly simplifies the solution of equations in physics, since it is a scalar theory, with applications and derivatives that apply elementary calculus.
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1. Introduction.__________________________________________________ 3
2. Newtonian mechanics.____________________________________________ 5
2.1. Newton's laws of motion.______________________________________________ 5
2.1.1. Newton's first law.________________________________________________ 6
2.1.2. Newton's second law.________________________________________________ 7
2.1.3. Newton's third law._________________________________________________ 8
2.2. The law of universal gravitation. ___________________________________________ 11
2.3. The main task of mechanics._____________________________________________ 13
2.4. Limits of applicability._______________________________________________ 15
3. Conclusion.______________________________________________ 18
4. List of references.______________________________________ 20
Newton (1643-1727)
This world was shrouded in deep darkness.
Let there be light! And here comes Newton.
1. Introduction.
The concept of "physics" has its roots in the deep past, in Greek it means "nature". The main task of this science is to establish the "laws" of the surrounding world. One of the main works of Plato, a student of Aristotle, was called "Physics".
The science of those years had a natural-philosophical character, i.e. proceeded from the fact that the directly observed movements of celestial bodies are their actual movements. From this, a conclusion was drawn about the central position of the Earth in the Universe. This system correctly reflected some of the features of the Earth as a celestial body: the fact that the Earth is a ball, that everything gravitates towards its center. Thus, this doctrine was actually about the Earth. At the level of its time, it met the basic requirements for scientific knowledge. Firstly, it explained the observed movements of celestial bodies from a unified point of view and, secondly, made it possible to calculate their future positions. In the same time theoretical constructions the ancient Greeks were purely speculative in nature - they were completely divorced from the experiment.
Such a system existed until the 16th century, before the advent of the teachings of Copernicus, which received its further substantiation in the experimental physics of Galileo, culminating in the creation of Newtonian mechanics, which united the movement of celestial bodies and terrestrial objects with unified laws of motion. It came the greatest revolution in natural science, which marked the beginning of the development of science in its modern sense.
Galileo Galilei believed that the world is infinite and matter is eternal. In all processes, nothing is destroyed or generated - there is only a change in the relative position of bodies or their parts. Matter consists of absolutely indivisible atoms, its movement is the only universal mechanical movement. The heavenly bodies are similar to the Earth and obey the same laws of mechanics.
For Newton, it was important to unambiguously find out, with the help of experiments and observations, the properties of the object under study and to build a theory based on induction without using hypotheses. He proceeded from the fact that in physics as an experimental science there is no place for hypotheses. Recognizing the imperfection of the inductive method, he considered it the most preferable among others.
Both in the era of antiquity and in the 17th century, the importance of studying the movement of heavenly bodies was recognized. But if for the ancient Greeks this problem had more philosophical significance, then for the 17th century, the practical aspect was predominant. The development of navigation necessitated the development of more accurate astronomical tables for navigation purposes than those required for astrological purposes. The main task was to determine the longitude, so necessary for astronomers and navigators. To solve this important practical problem, the first state observatories were created (in 1672, Paris, in 1675, Greenwich). In essence, this was the task of determining absolute time, which, when compared with local time, gave a time interval that could be converted into longitude. It was possible to determine this time by observing the movements of the Moon among the stars, as well as with the help of an accurate clock set in absolute time and held by the observer. For the first case, very accurate tables were needed to predict the position of celestial bodies, and for the second, absolutely accurate and reliable watch mechanisms. Work in these directions was not successful. Only Newton succeeded in finding a solution, who, thanks to the discovery of the law of universal gravitation and the three basic laws of mechanics, as well as differential and integral calculus, gave mechanics the character of an integral scientific theory.
2. Newtonian mechanics.
The pinnacle of I. Newton's scientific work is his immortal work "The Mathematical Principles of Natural Philosophy", first published in 1687. In it, he summarized the results obtained by his predecessors and his own research and created for the first time a unified harmonious system of terrestrial and celestial mechanics, which formed the basis of all classical physics. Here Newton gave definitions of the initial concepts - the amount of matter, equivalent to mass, density; amount of motion equivalent to momentum, and various kinds strength. Formulating the concept of quantity of matter, he proceeded from the idea that atoms consist of some single primary matter; Density was understood as the degree to which a unit volume of a body is filled with primary matter. This work outlines Newton's doctrine of universal gravitation, on the basis of which he developed the theory of the motion of planets, satellites and comets that form the solar system. Based on this law, he explained the phenomenon of tides and the compression of Jupiter.
Newton's concept was the basis for many technical advances over a long period of time. Many methods of scientific research were formed on its foundation. various fields natural sciences.
2.1. Newton's laws of motion.
If kinematics studies the movement of a geometric body, which does not have any properties of a material body, except for the ability to occupy a certain place in space and change this position over time, then dynamics studies the movement of real bodies under the action of forces applied to them. The three laws of mechanics established by Newton underlie dynamics and form the main section of classical mechanics.
They can be directly applied to the simplest case of motion, when the moving body is considered as a material point, i.e. when the size and shape of the body is not taken into account and when the movement of the body is considered as the movement of a point with mass. In boiling water, to describe the movement of a point, you can choose any coordinate system, relative to which the quantities characterizing this movement are determined. Any body moving relative to other bodies can be taken as a reference body. In dynamics, one deals with inertial coordinate systems, characterized by the fact that relative to them a free material point moves at a constant speed.
2.1.1. Newton's first law.
The law of inertia was first established by Galileo for the case of horizontal motion: when a body moves along a horizontal plane, its motion is uniform and would continue constantly if the plane extended in space without end. Newton gave a more general formulation of the law of inertia as the first law of motion: every body is in a state of rest or uniform rectilinear motion until the forces acting on it change this state.
In life, this law describes the case when, if you stop pulling or pushing a moving body, then it stops, and does not continue to move at a constant speed. So the car with the engine off stops. According to Newton's law, a braking force must act on a car rolling by inertia, which in practice is air resistance and the friction of car tires on the surface of the highway. They tell the car a negative acceleration until it stops.
The disadvantage of this formulation of the law is that it did not contain an indication of the need to refer motion to an inertial coordinate system. The fact is that Newton did not use the concept of an inertial coordinate system - instead, he introduced the concept of absolute space - homogeneous and immobile - with which he connected a certain absolute coordinate system, relative to which the speed of the body was determined. When the emptyness of absolute space as an absolute reference system was revealed, the law of inertia began to be formulated differently: with respect to the inertial coordinate system, a free body maintains a state of rest or uniform rectilinear motion.
2.1.2. Newton's second law.
In the formulation of the second law, Newton introduced the concepts:
Acceleration - vector quantity(Newton called it momentum and took it into account when formulating the parallelogram rule of velocities), which determines the rate of change in the speed of a body.
Force is a vector quantity, understood as a measure of mechanical action on the body by other bodies or fields, as a result of which the body acquires acceleration or changes its shape and size.
The mass of a body is a physical quantity, one of the main characteristics of matter, which determines its inertial and gravitational properties.
The second law of mechanics says: the force acting on a body is equal to the product of the mass of the body and the acceleration imparted by this force. This is its modern formulation. Newton formulated it differently: the change in momentum is proportional to the applied operating force and occurs in the direction of the straight line along which this force acts, and inversely proportional to the mass of the body or mathematically:
It is easy to confirm this law by experience, if a trolley is attached to the end of the spring and the spring is released, then in time t the cart will pass the way s 1(Fig. 1), then attach two carts to the same spring, i.e. double the body weight, and release the spring, then in the same time t they will go the way s2, two times smaller than s 1 .
This law is also valid only in inertial frames of reference. From a mathematical point of view, the first law is a special case of the second law, because if the resultant forces are zero, then the acceleration is also zero. However, Newton's first law is considered as an independent law, because it is he who asserts the existence of inertial systems.
2.1.3. Newton's third law.
Newton's third law says: there is always an equal and opposite reaction to an action, otherwise the bodies act on each other with forces directed along one straight line, equal in magnitude and opposite in direction or mathematically:
Newton extended the operation of this law to the case of collisions of bodies, and to the case of their mutual attraction. The simplest demonstration of this law is a body located on a horizontal plane, on which the force of gravity acts F t and support reaction force F about, lying on one straight line, equal in value and oppositely directed, the equality of these forces allows the body to be at rest (Fig. 2).
Consequences follow from Newton's three fundamental laws of motion, one of which is the addition of momentum according to the parallelogram rule. The acceleration of a body depends on the quantities that characterize the action of other bodies on a given body, as well as on the quantities that determine the features of this body. The mechanical action on the body from other bodies, which changes the speed of movement of this body, is called force. It can have a different nature (gravity, elasticity, etc.). The change in the speed of a body does not depend on the nature of the forces, but on their magnitude. Since speed and force are vectors, the action of several forces is added according to the parallelogram rule. The property of a body, on which the acceleration acquired by it depends, is inertia, measured by mass. In classical mechanics, dealing with speeds much less than the speed of light, mass is a characteristic of the body itself, regardless of whether it is moving or not. The mass of a body in classical mechanics does not depend on the interaction of the body with other bodies either. This property of mass prompted Newton to accept mass as a measure of matter and to believe that its magnitude determines the amount of matter in the body. Thus, mass began to be understood as the amount of matter.
The amount of matter is measurable, being proportional to the weight of the body. Weight is the force with which a body acts on a support that prevents it from falling freely. Numerically, the weight is equal to the product of the mass of the body and the acceleration of gravity. Due to the compression of the Earth and its daily rotation, body weight changes with latitude and is 0.5% less at the equator than at the poles. Since mass and weight are strictly proportional, it turned out to be possible to practically measure the mass or quantity of matter. The understanding that weight is a variable effect on the body prompted Newton to establish the internal characteristic of the body - inertia, which he considered as the body's inherent ability to maintain uniform rectilinear motion proportional to the mass. Mass as a measure of inertia can be measured with a balance, as did Newton.
In a state of weightlessness, mass can be measured by inertia. Inertia measurement is in a general way mass measurements. But inertia and weight are different physical concepts. Their proportionality to each other is very convenient in practical terms - for measuring mass with the help of scales. Thus, the establishment of the concepts of force and mass, as well as the method of their measurement, allowed Newton to formulate the second law of mechanics.
The first and second laws of mechanics refer respectively to the motion of a material point or one body. In this case, only the action of other bodies on this body is taken into account. However, every action is an interaction. Since in mechanics action is characterized by force, if one body acts on another with a certain force, then the second acts on the first with the same force, which fixes the third law of mechanics. In Newton's formulation, the third law of mechanics is valid only for the case of direct interaction of forces or for the instantaneous transfer of the action of one body to another. In the case of transferring an action over a finite period of time, this law applies when the time of transferring the action can be neglected.
2.2. The law of universal gravitation.
It is believed that the core of Newton's dynamics is the concept of force, and the main task of dynamics is to establish a law from a given movement and, conversely, to determine the law of motion of bodies according to a given force. From Kepler's laws, Newton deduced the existence of a force directed towards the Sun, which was inversely proportional to the square of the distance of the planets from the Sun. Generalizing the ideas expressed by Kepler, Huygens, Descartes, Borelli, Hooke, Newton gave them the exact form of a mathematical law, according to which the existence of a force of universal gravitation in nature, which determines the attraction of bodies, was affirmed. The force of gravity is directly proportional to the product of the masses of gravitating bodies and inversely proportional to the square of the distance between them, or mathematically:
Where G is the gravitational constant.
This law describes the interaction of any bodies - it is only important that the distance between the bodies be large enough compared to their sizes, this allows us to take bodies for material points. In the Newtonian theory of gravitation, it is assumed that the gravitational force is transferred from one gravitating body to another instantly, and without the mediation of any medium. The law of universal gravitation has caused long and furious discussions. This was not accidental, since this law had an important philosophical significance. The bottom line was that before Newton, the goal of creating physical theories was the identification and presentation of the mechanism of physical phenomena in all its details. In cases where this could not be done, the argument was put forward about the so-called "hidden qualities", which are not amenable to detailed interpretation. Bacon and Descartes declared references to "hidden qualities" to be unscientific. Descartes believed that it is possible to understand the essence of a natural phenomenon only if it is visually imagined. Thus, he represented the phenomena of gravity with the help of ethereal vortices. In the context of the widespread use of such ideas, Newton's law of universal gravitation, despite the fact that it demonstrated the correspondence of astronomical observations made on its basis with unprecedented accuracy, was questioned on the ground that the mutual attraction of bodies was very reminiscent of the peripatetic doctrine of "hidden qualities." And although Newton established the fact of its existence on the basis of mathematical analysis and experimental data, mathematical analysis has not yet become firmly established in the minds of researchers as a sufficiently reliable method. But the desire to limit physical research to facts that do not claim to be absolute truth allowed Newton to complete the formation of physics as an independent science and separate it from natural philosophy with its claims to absolute knowledge.
In the law of universal gravitation, science received an example of the law of nature as an absolutely precise rule applicable everywhere, without exception, with precisely defined consequences. This law was included by Kant in his philosophy, where nature was represented as the realm of necessity as opposed to morality - the realm of freedom.
Newton's physical concept was a kind of crowning achievement of 17th century physics. The static approach to the universe has been replaced by a dynamic one. The experimental-mathematical method of research, having made it possible to solve many problems of physics of the 17th century, turned out to be suitable for solving physical problems for another two centuries.
2.3. The main task of mechanics.
The result of the development of classical mechanics was the creation of a unified mechanical picture of the world, within which the entire qualitative diversity of the world was explained by differences in the movement of bodies, subject to the laws of Newtonian mechanics. According to the mechanical picture of the world, if the physical phenomenon of the world could be explained on the basis of the laws of mechanics, then such an explanation was recognized as scientific. Newtonian mechanics thus became the basis of the mechanical picture of the world that dominated until the scientific revolution at the turn of the 19th and 20th centuries.
Newton's mechanics, in contrast to previous mechanical concepts, made it possible to solve the problem of any stage of motion, both preceding and subsequent, and at any point in space when known facts, causing this movement, as well as the inverse problem of determining the magnitude and direction of these factors at any point with known basic elements of the movement. Because of this, Newtonian mechanics could be used as a method for the quantitative analysis of mechanical motion. Any physical phenomena could be studied as, regardless of the factors causing them. For example, you can calculate the speed of an Earth satellite: For simplicity, let's find the speed of a satellite with an orbit equal to the radius of the Earth (Fig. 3). With sufficient accuracy, we can equate the acceleration of the satellite to the acceleration of free fall on the surface of the Earth:
On the other hand, the centripetal acceleration of the satellite.
where 
. This speed is called the first cosmic speed. A body of any mass, to which such a speed will be communicated, will become a satellite of the Earth.
The laws of Newtonian mechanics associated force not with motion, but with a change in motion. This made it possible to abandon the traditional notion that force is needed to maintain movement, and to divert friction, which made force necessary in operating mechanisms to maintain movement, to a secondary role. Having established a dynamic view of the world instead of the traditional static one, Newton made his dynamics the basis of theoretical physics. Although Newton was cautious in his mechanical interpretations natural phenomena, still considered it desirable to deduce other natural phenomena from the principles of mechanics. Further development physics began to be carried out in the direction of further development of the apparatus of mechanics in relation to the solution of specific problems, as they were solved, the mechanical picture of the world was strengthened.
2.4. Limits of applicability.
As a result of the development of physics at the beginning of the 20th century, the scope of classical mechanics was determined: its laws are valid for motions whose speed is much less than the speed of light. It was found that with increasing speed, body weight increases. In general, Newton's laws of classical mechanics are valid for the case of inertial frames of reference. In the case of non-inertial frames of reference, the situation is different. With the accelerated movement of a non-inertial coordinate system relative to the inertial system, Newton's first law (the law of inertia) does not take place in this system - free bodies in it will change their speed of movement over time.
The first inconsistency in classical mechanics was revealed when the microworld was discovered. In classical mechanics, displacements in space and the determination of velocity were studied regardless of how these displacements were realized. With regard to the phenomena of the microworld, such a situation, as it turned out, is impossible in principle. Here the spatio-temporal localization underlying the kinematics is possible only for some particular cases, which depend on the specific dynamic conditions of motion. On a macro scale, the use of kinematics is quite acceptable. For micro scales, where the main role belongs to quanta, kinematics, which studies motion regardless of dynamic conditions, loses its meaning.
For the scales of the microworld, Newton's second law turned out to be untenable - it is valid only for large-scale phenomena. It turned out that attempts to measure any quantity characterizing the system under study entails an uncontrolled change in other quantities characterizing this system: if an attempt is made to establish the position in space and time, this leads to an uncontrolled change in the corresponding conjugate quantity, which determines the dynamic state systems. Thus, it is impossible to accurately measure two mutually conjugate quantities at the same time. The more precisely the value of one quantity characterizing the system is determined, the more uncertain is the value of its conjugate quantity. This circumstance entailed a significant change in views on the understanding of the nature of things.
The discrepancy in classical mechanics came from the fact that the future in a certain sense is completely contained in the present - this determines the possibility of accurately predicting the behavior of the system at any future moment of time. This possibility offers the simultaneous determination of mutually conjugate quantities. In the field of the microcosm, this turned out to be impossible, which introduces significant changes in the understanding of the possibilities of foresight and the relationship of natural phenomena: since the value of the quantities characterizing the state of the system at a certain point in time can only be established with a certain degree of uncertainty, then the possibility of accurately predicting the values of these quantities in subsequent periods is excluded. points in time, i.e. one can only predict the probability of obtaining certain values.
Another discovery that shook the foundations of classical mechanics was the creation of field theory. Classical mechanics tried to reduce all natural phenomena to the forces acting between the particles of matter - this was the basis of the concept electrical fluids. Within this concept were real only substance and its changes - here the description of the action of two electric charges with the help of concepts related to them was recognized as the most important. The description of the field between these charges, and not of the charges themselves, was very essential for understanding the action of the charges. Here is a simple example of violation of Newton's third law under such conditions: if a charged particle moves away from a conductor through which current flows, and accordingly a magnetic field is created around it, then the resulting force acting from the charged particle on the conductor with current is exactly zero.
The created new reality had no place in the mechanical picture of the world. As a result, physics began to deal with two realities - matter and field. If classical physics was based on the concept of matter, then with the revelation of a new reality, the physical picture of the world had to be revised. Attempts to explain electromagnetic phenomena with the help of the ether turned out to be untenable. The ether has not been found experimentally. This led to the creation of the theory of relativity, which forced us to reconsider the ideas about space and time that are characteristic of classical physics. Thus, two concepts - the theory of quanta and the theory of relativity - became the foundation for new physical concepts.
3. Conclusion.
The contribution made by Newton to the development of natural science was that he gave a mathematical method of converting physical laws into quantitatively measurable results that could be confirmed by observations, and, conversely, deduce physical laws based on such observations. As he himself wrote in the preface to the "Principles", "... we propose this work as the mathematical foundations of physics. The whole difficulty of physics ... lies in recognizing the forces of nature by the phenomena of motion, and then using these forces to explain the rest of the phenomena ... It would be desirable to derive from the principles of mechanics the rest of the phenomena of nature, arguing in a similar way, for many things make me suppose that all these phenomena are determined by certain forces with which the particles of bodies, due to reasons still unknown, or tend to each other and cleave into regular figures, or mutually repulse and move away from each other. Since these forces are unknown, until now the attempts of philosophers to explain the phenomena of nature have remained fruitless. I hope, however, that either this way of reasoning, or another, more correct, the grounds set forth here will provide some illumination."
The Newtonian method has become the main tool for understanding nature. The laws of classical mechanics and methods of mathematical analysis demonstrated their effectiveness. physical experiment, relying on measuring technology, provided unprecedented accuracy. Physical knowledge increasingly became the basis of industrial technology and technology, stimulated the development of other natural sciences. In physics, previously isolated light, electricity, magnetism and heat were united in the electromagnetic theory. And although the nature of gravity remained unexplained, its effects could be calculated. The concept of Laplace's mechanistic determinism was established, based on the possibility to uniquely determine the behavior of the system at any time, given the known initial conditions. The structure of mechanics as a science seemed solid, reliable and almost completely complete - i.e. the phenomena that did not fit into the existing classical canons, which one had to deal with, seemed quite explicable in the future by more sophisticated minds from the standpoint of classical mechanics. One got the impression that the knowledge of physics was close to its full completion - such a powerful force was demonstrated by the foundation of classical physics.
4. List of references.
1. Karpenkov S.Kh. Basic concepts of natural science. M.: UNITI, 1998.
2. Newton and philosophical problems of physics of the XX century. A team of authors, ed. M.D. Akhundova, S.V. Illarionov. M.: Nauka, 1991.
3. Gursky I.P. Elementary physics. Moscow: Nauka, 1984.
4. Great Soviet Encyclopedia in 30 volumes. Ed. Prokhorova A.M., 3rd edition, M., Soviet Encyclopedia, 1970.
5. Dorfman Ya.G. The World History physics with early XIX until the middle of the 20th century. M., 1979.
S. Marshak, Op. in 4 volumes, Moscow, Goslitizdat, 1959, v. 3, p. 601
Cit. Quoted from: Bernal J. Science in the history of society. M., 1956.S.265
classical mechanics- a type of mechanics (a branch of physics that studies the laws of change in the positions of bodies in space over time and the causes that cause it), based on Newton's laws and Galileo's principle of relativity. Therefore, it is often called Newtonian mechanics».
Classical mechanics is subdivided into:
- statics (which considers the equilibrium of bodies)
- kinematics (which studies the geometric property of motion without considering its causes)
- dynamics (which considers the movement of bodies).
There are several equivalent ways to formally describe classical mechanics mathematically:
- Lagrangian formalism
- Hamiltonian formalism
Classical mechanics gives very accurate results if its application is limited to bodies whose speeds are much less than the speed of light, and whose dimensions are much larger than the sizes of atoms and molecules. A generalization of classical mechanics to bodies moving at an arbitrary speed is relativistic mechanics, and to bodies whose dimensions are comparable to atomic ones - quantum mechanics. Quantum field theory considers quantum relativistic effects.
Nevertheless, classical mechanics retains its value because:
- it is much easier to understand and use than other theories
- in a wide range, it describes reality quite well.
Classical mechanics can be used to describe the motion of objects such as tops and baseballs, many astronomical objects (such as planets and galaxies), and sometimes even many microscopic objects such as molecules.
Classical mechanics is a self-consistent theory, that is, within its framework there are no statements that contradict each other. However, its association with other classical theories, for example, classical electrodynamics and thermodynamics leads to the appearance of insoluble contradictions. In particular, classical electrodynamics predicts that the speed of light is constant for all observers, which is inconsistent with classical mechanics. At the beginning of the 20th century, this led to the need to create a special theory of relativity. When considered together with thermodynamics, classical mechanics leads to the Gibbs paradox, in which it is impossible to accurately determine the amount of entropy, and to the ultraviolet catastrophe, in which a blackbody must radiate an infinite amount of energy. Attempts to solve these problems led to the emergence and development of quantum mechanics.
Basic concepts
Classical mechanics operates with several basic concepts and models. Among them should be highlighted:
Basic Laws
Galileo's principle of relativity
The basic principle on which classical mechanics is based is the principle of relativity, formulated on the basis of empirical observations by G. Galileo. According to this principle, there are infinitely many frames of reference in which a free body is at rest or moves with a constant speed in absolute value and direction. These frames of reference are called inertial and move relative to each other uniformly and rectilinearly. In all inertial frames of reference, the properties of space and time are the same, and all processes in mechanical systems obey the same laws. This principle can also be formulated as the absence of absolute reference systems, that is, reference systems that are somehow distinguished relative to others.
Newton's laws
Newton's three laws are the basis of classical mechanics.
Newton's second law is not enough to describe the motion of a particle. Additionally, a description of the force is required, obtained from consideration of the essence of the physical interaction in which the body participates.
Law of energy conservation
The law of conservation of energy is a consequence of Newton's laws for closed conservative systems, that is, systems in which only conservative forces act. From a more fundamental point of view, there is a relationship between the law of conservation of energy and the homogeneity of time, expressed by Noether's theorem.
Beyond the applicability of Newton's laws
Classical mechanics also includes descriptions complex movements extended non-point objects. Euler's laws provide an extension of Newton's laws to this area. The concept of angular momentum is based on the same mathematical methods used to describe one-dimensional motion.
The equations of rocket motion expand the concept of velocity when an object's momentum changes over time to account for such effects as mass loss. There are two important alternative formulations of classical mechanics: Lagrange mechanics and Hamiltonian mechanics. These and other modern formulations tend to bypass the concept of "force", and emphasize other physical quantities, such as energy or action, to describe mechanical systems.
The above expressions for momentum and kinetic energy are valid only in the absence of a significant electromagnetic contribution. In electromagnetism, Newton's second law for a wire carrying current is violated if it does not include the contribution of the electromagnetic field to the momentum of the system expressed in terms of the Poynting vector divided by c 2 , where c is the speed of light in free space.
Story
ancient time
Classical mechanics originated in antiquity mainly in connection with the problems that arose during construction. The first of the sections of mechanics to be developed was statics, the foundations of which were laid in the works of Archimedes in the 3rd century BC. e. He formulated the rule of the lever, the theorem on the addition of parallel forces, introduced the concept of center of gravity, laid the foundations of hydrostatics (Archimedes force).
Middle Ages
new time
17th century
18th century
19th century
In the 19th century, the development of analytical mechanics takes place in the works of Ostrogradsky, Hamilton, Jacobi, Hertz, and others. In the theory of vibrations, Routh, Zhukovsky, and Lyapunov developed a theory of the stability of mechanical systems. Coriolis developed the theory of relative motion by proving the acceleration theorem. In the second half of the 19th century, kinematics was separated into a separate section of mechanics.
Particularly significant in the 19th century were advances in continuum mechanics. Navier and Cauchy formulated the equations of elasticity theory in a general form. In the works of Navier and Stokes, differential equations of hydrodynamics were obtained taking into account the viscosity of the liquid. Along with this, there is a deepening of knowledge in the field of hydrodynamics of an ideal fluid: the works of Helmholtz on vortices, Kirchhoff, Zhukovsky and Reynolds on turbulence, and Prandtl on boundary effects appear. Saint-Venant developed a mathematical model describing the plastic properties of metals.
Newest time
In the 20th century, the interest of researchers switched to nonlinear effects in the field of classical mechanics. Lyapunov and Henri Poincaré laid the foundations for the theory of nonlinear oscillations. Meshchersky and Tsiolkovsky analyzed the dynamics of bodies of variable mass. Aerodynamics stands out from continuum mechanics, the foundations of which were developed by Zhukovsky. In the middle of the 20th century, a new direction in classical mechanics is actively developing - the theory of chaos. The issues of stability of complex dynamical systems also remain important.
Limitations of classical mechanics
Classical mechanics gives accurate results for the systems we encounter in everyday life. But her predictions become incorrect for systems approaching the speed of light, where it is replaced by relativistic mechanics, or for very small systems where the laws of quantum mechanics apply. For systems that combine both of these properties, relativistic mechanics is used instead of classical mechanics. quantum theory fields. For systems with very big amount components, or degrees of freedom, classical mechanics also cannot be adequate, but methods of statistical mechanics are used.
Classical mechanics is widely used because, firstly, it is much simpler and easier to apply than the theories listed above, and, secondly, it has great possibilities for approximation and application for a very wide class of physical objects, starting from the usual, such as a spinning top or a ball, to large astronomical objects (planets, galaxies) and very microscopic ones (organic molecules).
Although classical mechanics is generally compatible with other "classical" theories such as classical electrodynamics and thermodynamics, there are some inconsistencies between these theories that were found in the late 19th century. They can be solved by methods more modern physics. In particular, the equations of classical electrodynamics are not invariant under Galilean transformations. The speed of light enters them as a constant, which means that classical electrodynamics and classical mechanics could only be compatible in one chosen frame of reference associated with the ether. However, experimental verification did not reveal the existence of the ether, which led to the creation of a special theory of relativity, in which the equations of mechanics were modified. The principles of classical mechanics are also inconsistent with some of the claims of classical thermodynamics, leading to the Gibbs paradox, according to which it is impossible to accurately determine the entropy, and to the ultraviolet catastrophe, in which absolutely black body must radiate an infinite amount of energy. To overcome these incompatibilities, quantum mechanics was created.
Notes
Internet links
- Video lecture 1. Physics: Classical mechanics (autumn 1999)// MIT Lectures: 8.01
Literature
- Arnold V.I. Avets A. Ergodic problems of classical mechanics. - RHD, 1999. - 284 p.
- B. M. Yavorsky, A. A. Detlaf. Physics for high school students and those entering universities. - M .: Academy, 2008. - 720 p. -( Higher education). - 34,000 copies. - ISBN 5-7695-1040-4
- Sivukhin D.V. General course of physics. - 5th edition, stereotypical. - M .: Fizmatlit, 2006. - T. I. Mechanics. - 560 p. - ISBN 5-9221-0715-1
- A. N. MATVEEV Mechanics and the Theory of Relativity. - 3rd ed. - M .: ONYX 21st century: World and Education, 2003. - 432 p. - 5000 copies. - ISBN 5-329-00742-9
- C. Kittel, W. Knight, M. Ruderman Mechanics. Berkeley Physics Course. - M .: Lan, 2005. - 480 p. - (Textbooks for universities). - 2000 copies. - ISBN 5-8114-0644-4
“Think of the benefit that good examples bring us, and you will find that the memory of great people is no less useful than their presence”
Mechanics is one of the most ancient Sciences. It arose and developed under the influence public practice requests and also thanks to abstracting activity of human thinking. Even in prehistoric times, people created buildings and observed the movement of various bodies. Many laws of mechanical motion and balance of material bodies were known by mankind through repeated repetitions, purely experimentally. This socio-historical experience, passed down from generation to generation, and was the the source material on the analysis of which mechanics as a science developed. The emergence and development of mechanics was closely associated with production, With needs human society. “At a certain stage in the development of agriculture,” writes Engels, “and in certain countries (raising water for irrigation in Egypt), and especially along with the emergence of cities, large buildings and the development of handicrafts, developed and Mechanics. Soon it also becomes necessary for shipping and military affairs.
First the manuscripts and scientific reports in the field of mechanics that have survived to this day belong to ancient scholars of Egypt and Greece. The oldest papyri and books, in which studies of some of the simplest problems of mechanics have been preserved, relate mainly to various problems. statics, i.e. the doctrine of balance. First of all, here it is necessary to name the works of the outstanding philosopher ancient greece(384-322 BC), who introduced the name into scientific terminology Mechanics for a wide field of human knowledge, in which the simplest movements of material bodies, observed in nature and created by man during his activities, are studied.
Aristotle was born in the Greek colony of Stagira in Thrace. His father was a physician to the Macedonian king. In 367, Aristotle settled in Athens, where he received a philosophical education at the Academy of the famous idealist philosopher in Greece. Plato. In 343 Aristotle took over teacher of Alexander the Great(Alexander the Great said: “I honor Aristotle on a par with my father, since if I owe my life to my father, then I owe Aristotle everything that gives her a price”), later the famous commander ancient world. His philosophical school, called the school peripatetics, Aristotle founded in 335 in Athens. Some philosophical provisions of Aristotle have not lost their significance to the present day. F. Engels wrote; "The ancient Greek philosophers were all born elemental dialecticians, and Aristotle, the most universal head among them, has already explored all the essential forms of dialectical thinking." But in the field of mechanics, these broad universal laws of human thinking did not receive a fruitful reflection in the works of Aristotle.
Archimedes owns a large number technical inventions, including the simplest water-lifting machine (archimedean screw), which has found application in Egypt for draining cultivated lands flooded with water. He showed himself as military engineer while protecting your hometown Syracuse (Sicily). Archimedes understood the power and great importance for humanity of accurate and systematic scientific research, and proud words are attributed to him: Give me a place to stand on and I will move the earth."
Archimedes was killed by the sword of a Roman soldier during the massacre arranged by the Romans during the capture of Syracuse. Tradition says that Archimedes, immersed in contemplation geometric shapes, said to the soldier who approached him: "Do not touch my drawings." The soldier, seeing in these words an insult to the power of the victors, cut off his head, and the blood of Archimedes stained his scientific work.
famous ancient astronomer Ptolemy(II century AD - there is evidence that Ptolemy (Claudius Ptolemaeus) lived and worked in Alexandria from 127 to 141 or 151. According to Arabic legend, he died at the age of 78.) in his work " The Great Mathematical Construction of Astronomy in 13 Books"developed a geocentric system of the world, in which the apparent movements of the firmament and planets were explained on the assumption that the Earth is motionless and is at the center of the universe. The entire firmament makes a complete revolution around the Earth in 24 hours, and the stars participate only in the daily movement, while maintaining their relative position unchanged; planets, moreover, move relative to the celestial sphere, changing their position relative to the stars. The laws of the apparent motions of the planets were established by Ptolemy to such an extent that it became possible to predict their positions relative to the sphere of the fixed stars.
However, the theory of the structure of the universe, created by Ptolemy, was erroneous; it led to extraordinarily complex and artificial schemes of the motion of the planets and in a number of cases could not fully explain their apparent movements relative to the stars. Particularly large inconsistencies between calculations and observations were obtained with predictions of solar and lunar eclipses made many years ahead.
Ptolemy did not adhere strictly to the methodology of Aristotle and conducted systematic experiments on the refraction of light. Physiological-optical observations Ptolemy have not lost their interest to date. The angles of light refraction found by him during the transition from air to water, from air to glass and from water to glass were very accurate for its time. Ptolemy remarkably combined strict mathematician and subtle experimenter.
In the era of the Middle Ages, the development of all sciences, as well as mechanics, was strongly slowed down. Moreover, during these years the most valuable monuments of science, technology and art of the ancients were destroyed and destroyed. Religious fanatics wiped out all the achievements of science and culture from the face of the earth. Most of the scientists of this period blindly adhered to the scholastic method of Aristotle in the field of mechanics, considering all the provisions contained in the writings of this scientist to be unconditionally correct. The geocentric system of the world of Ptolemy was canonized. Speech against this system of the world and the main provisions of the philosophy of Aristotle were considered a violation of the foundations scripture, and researchers who decided to do this were announced heretics. “The priesthood killed the living in Aristotle and immortalized the dead,” wrote Lenin. Dead, empty scholasticism filled the pages of many treatises. Ridiculous problems were posed, and exact knowledge was persecuted and withered. A large number of works on mechanics in the Middle Ages were devoted to finding " perpetuum mobile”, i.e. perpetual motion machine operating without receiving energy from outside. These works, for the most part, contributed little to the development of mechanics (Mohammed well expressed the ideology of the Middle Ages, saying: "If the sciences teach what is written in the Koran, they are superfluous; if they teach otherwise, they are godless and criminal"). “The Christian Middle Ages left nothing to science,” says F. Engels in Dialectics of Nature.
The intensive development of mechanics began in renaissance from the beginning of the 15th century in Italy, and then in other countries. In this era, especially great progress in the development of mechanics was achieved thanks to the work (1452-1519), (1473-1543) and Galilee (1564-1642).
Famous Italian painter, mathematician, mechanic and engineer, Leonardo da Vinci engaged in research on the theory of mechanisms (he built an elliptical lathe), studied friction in machines, investigated the movement of water in pipes and the movement of bodies along an inclined plane. He was the first to recognize the extreme importance of the new concept of mechanics - the moment of force relative to a point. Investigating the balance of forces acting on the block, he established that the role of the shoulder of force is played by the length of the perpendicular dropped from the fixed point of the block to the direction of the rope carrying the load. The equilibrium of the block is possible only if the products of forces and the lengths of the corresponding perpendiculars are equal; in other words, the equilibrium of the block is possible only under the condition that the sum of the static moments of forces relative to the weight gain point of the block will be equal to zero.
A revolutionary revolution in the views on the structure of the universe was carried out by a Polish scientist who, as figuratively written on his monument in Warsaw, "stopped the Sun and moved the Earth." new, heliocentric system of the world explained the movement of the planets, based on the fact that the Sun is a fixed center, around which all the planets move in circles. Here are the original words of Copernicus, taken from his immortal work: “What appears to us as the movement of the Sun does not come from its movement, but from the movement of the Earth and its sphere, with which we revolve around the Sun, like any other planet. So, the Earth has more than one movement. The apparent simple and retrograde motions of the planets are not due to their motion, but to the motion of the Earth. Thus, one movement of the Earth is sufficient to explain so many apparent inequalities in the sky.
In the work of Copernicus was revealed main feature movements of the planets and calculations are given relating to the predictions of solar and lunar eclipses. The explanations of the apparent return motions of Mercury, Venus, Mars, Jupiter, and Saturn relative to the sphere of the fixed stars have acquired clarity, distinctness, and simplicity. Copernicus clearly understood the kinematics of the relative motion of bodies in space. He writes: “Every perceived change in position occurs due to the movement of either the observed object or the observer, or due to the movement of both, if, of course, they are different from each other; for when the observed object and the observer move in the same way and in the same direction, no movement is noticed between the observed object and the observer.
Truly scientific Copernican theory made it possible to obtain a number of important practical results: to increase the accuracy of astronomical tables, to reform the calendar (introducing a new style), and to determine the length of the year more strictly.
Works of the brilliant Italian scientist Galilee were fundamental to the development speakers.
Dynamics as a science was founded by Galileo, who discovered many very important properties of uniformly accelerated and uniformly slow motions. The foundations of this new science were set forth by Galileo in a book entitled "Conversations and Mathematical Proofs Concerning Two New Branches of Science Relating to Mechanics and Local Motion." In chapter III, on dynamics, Galileo writes: “We are creating a new science, the subject of which is extremely old. In nature, there is nothing ancient movement, but it is precisely with regard to it that philosophers have written very little significant. Therefore, I have repeatedly studied its features by experience, which are quite deserving of this, but until now either unknown or unproven. So, for example, they say that the natural motion of a falling body is accelerated motion. However, the extent to which the acceleration increases has not yet been indicated; as far as I know, no one has yet proved that the spaces traversed by a falling body at the same time intervals are related to each other as successive odd numbers. It was also noticed that the thrown bodies or projectiles describe a certain curved line, but no one indicated that this line is a parabola.
Galileo Galilei (1564-1642)
Before Galileo, forces acting on bodies were usually considered in a state of equilibrium and the action of forces was measured only by static methods (lever, scales). Galileo pointed out that force is the cause of the change in speed, and thus established dynamic method comparison of forces. Galileo's research in the field of mechanics is important not only for the results that he managed to obtain, but also for his consistent introduction to mechanics. experimental movement research method.
So, for example, the law of isochronism of pendulum oscillations at small angles of deflection, the law of motion of a point along an inclined plane were investigated by Galileo through carefully staged experiments.
Thanks to the works of Galileo, the development of mechanics is firmly associated with the demands technology, And scientific experiment systematically introduced as fruitful research method phenomena of mechanical movement. Galileo in his conversations directly says that observing the work of the “first” masters in the Venetian arsenal and talking with them helped him understand “the causes of phenomena that were not only amazing, but also seemed at first completely unbelievable.” Many provisions of Aristotle's mechanics were specified by Galileo (as, for example, the law on the addition of motions) or very ingeniously refuted by purely logical reasoning (refutation by setting up experiments was considered insufficient at that time). We present here Galileo's proof to characterize the style. refuting Aristotle's position that heavy bodies on the surface of the Earth fall faster, and light bodies fall more slowly. The reasoning is given in the form of a conversation between a follower of Galileo (Salviati) and Aristotle (Simplicio):
« Salviati: ... Without further experience, by a brief but convincing reasoning, we can clearly show the incorrectness of the statement that heavier bodies move faster than lighter ones, implying bodies of the same substance, i.e. such as those of which Aristotle speaks . In fact, tell me, Señor Simplicio, do you admit that every falling body has a certain speed by nature, which can be increased or decreased only by introducing new strength or obstacles?
Simplicio: I have no doubt that the same body in the same medium has a constant speed, determined by nature, which cannot increase except from the application of a new force, or decrease except from an obstacle that slows down the movement.
Salviati: Thus, if we have two falling bodies, the natural speeds of which are different, and we combine the faster one with the slower one, then it is clear that the motion of the body falling faster will be somewhat delayed, and the motion of the other will be somewhat accelerated. Do you object to this position?
Simplicio: I think that this is quite correct.
Salviati: But if this is so, and if at the same time it is true that big Stone moves, say, with a speed of eight cubits, while the other, smaller one, with a speed of four cubits, then by joining them together, we should get a speed less than eight cubits; but two stones joined together make a body greater than the original, which had a speed of eight cubits; therefore, it turns out that a heavier body moves at a lower speed than a lighter one, and this is contrary to your assumption. You see now how, from the position that heavier bodies move faster than lighter ones, I could conclude that heavier bodies move less quickly.
The phenomena of a uniformly accelerated fall of a body on Earth were observed by numerous scientists before Galileo, but none of them could discover true reasons and the correct laws that explain these everyday phenomena. Lagrange notes on this occasion that "an extraordinary genius was needed to discover the laws of nature in such phenomena that were always before our eyes, but the explanation of which, nevertheless, always eluded the research of philosophers."
So, Galileo was the founder of modern dynamics. Galileo clearly understood the laws of inertia and independent action of forces in their modern form.
Galileo was an outstanding observing astronomer and an ardent supporter of the heliocentric worldview. Radically improving the telescope, Galileo discovered the phases of Venus, the satellites of Jupiter, spots on the Sun. He waged a persistent, consistently materialistic struggle against the scholasticism of Aristotle, the dilapidated system of Ptolemy, and the anti-scientific canons of the Catholic Church. Galileo is one of the great men of science, "who knew how to break the old and create the new, in spite of any obstacles, in spite of everything."
The works of Galileo were continued and developed (1629-1695), who developed the theory of oscillations of a physical pendulum and installed laws of action of centrifugal forces. Huygens extended the theory of accelerated and retarded motions of one point (translational motion of a body) to the case of a mechanical system of points. This was a significant step forward, as it allowed the study rotational movements solid body. Huygens introduced the concept of moment of inertia of the body about the axis and defined the so-called swing center" physical pendulum. When determining the swing center of a physical pendulum, Huygens proceeded from the principle that "a system of weighty bodies moving under the influence of gravity cannot move in such a way that the common center of gravity of the bodies rises above its original position." Huygens also showed himself as an inventor. He created the design of pendulum clocks, invented the balancer-regulator of the pocket watch, built the best astronomical tubes of that time and was the first to clearly see the ring of the planet Saturn.
Thus, the subject of study of classical mechanics is the laws and causes of mechanical motion, understood as the interaction of macroscopic (consisting of a huge number of particles) physical bodies and their constituent parts, and the change in their position in space generated by this interaction, occurring at subluminal (nonrelativistic) speeds.
The place of classical mechanics in the system of physical sciences and the limits of its applicability are shown in Figure 1.
Figure 1. Scope of applicability of classical mechanics
Classical mechanics is subdivided into statics (which considers the equilibrium of bodies), kinematics (which studies the geometric property of motion without considering its causes), and dynamics (which considers the movement of bodies taking into account the causes that cause it).
There are several equivalent ways of formal mathematical description of classical mechanics: Newton's laws, Lagrange formalism, Hamiltonian formalism, Hamilton-Jacobi formalism.
When classical mechanics is applied to bodies whose speeds are much less than the speed of light, and whose dimensions are much larger than those of atoms and molecules, and at distances or conditions where the speed of propagation of gravity can be considered infinite, it gives extremely accurate results. Therefore, today, classical mechanics retains its significance, since it is much easier to understand and use than other theories, and describes everyday reality quite well. Classical mechanics can be used to describe the motion of a very wide class of physical objects: both ordinary objects of the macrocosm (such as a spinning top and a baseball), and objects of astronomical dimensions (such as planets and stars), and many microscopic objects.
Classical mechanics is the oldest of the physical sciences. Even in pre-antique times, people not only experienced the laws of mechanics, but also applied them in practice, designing the simplest mechanisms. Already in the Neolithic and bronze age a wheel appeared, a little later a lever and an inclined plane were used. In the ancient period, the accumulated practical knowledge began to be generalized, the first attempts were made to define the basic concepts of mechanics, such as force, resistance, displacement, speed, and to formulate some of its laws. It was during the development of classical mechanics that the foundations were laid scientific method knowledge, which implies certain general rules for scientific reasoning about empirically observed phenomena, making assumptions (hypotheses) that explain these phenomena, building models that simplify the phenomena under study while maintaining their essential properties, forming systems of ideas or principles (theories) and their mathematical interpretation.
However, the qualitative formulation of the laws of mechanics began only in the 17th century AD. e., when Galileo Galilei discovered the kinematic law of addition of velocities and established the laws of free fall of bodies. A few decades after Galileo, Isaac Newton formulated the basic laws of dynamics. In Newtonian mechanics, the motion of bodies is considered at speeds much less than the speed of light in a vacuum. It is called classical or Newtonian mechanics, in contrast to relativistic mechanics, created at the beginning of the 20th century, mainly due to the work of Albert Einstein.
Modern classical mechanics, as a method of studying natural phenomena, uses their description with the help of a system of basic concepts and the construction on their basis of ideal models of real phenomena and processes.
