Definition 1

Mechanics is an extensive branch of physics that studies the laws of change in positions physical bodies in space and time, as well as postulates based on Newton's laws.

Figure 1. Basic law of dynamics. Author24 - online exchange of student papers

Often this scientific direction of physics is called "Newtonian mechanics". Classical mechanics today is divided into the following sections:

statics - considers and describes the balance of bodies;
kinematics - studies the geometric features of motion without considering its causes;
dynamics - deals with the study of the movement of material substances.

Mechanical motion is one of the simplest and at the same time the most common form of existence of living matter. Therefore, classical mechanics occupies an exceptionally significant place in natural science and is considered the main subsection of physics.

Basic laws of classical mechanics

Classical mechanics in its postulates studies the movement of working bodies, with speeds that are much less than the speed of light. According to the special hypothesis of relativity, there is no absolute space and time for elements moving at great speed. As a result, the nature of the interaction of substances becomes more complicated, in particular, their mass begins to depend on the speed of movement. All this has become an object of consideration for the formulas of relativistic mechanics, for which the light velocity constant plays a fundamental role.

Classical mechanics is based on the following fundamental laws.

Galileo's principle of relativity. According to this principle, there are many frames of reference in which any free body is at rest or moves with a constant speed in direction. These concepts in science are called inertial, and I move relative to each other in a straight line and uniformly.
Newton's three laws. The first establishes the obligatory presence of the property of inertness in physical bodies and postulates the presence of such reference concepts in which the movement of free matter occurs at a constant speed. The second postulate introduces the concept of force as the main measure of the interaction of active elements and, on the basis of theoretical facts, postulates the relationship between the acceleration of a body, its magnitude and inertia. Newton's third law - for every force acting on the first body, there is a counteracting factor equal in magnitude and opposite in direction.
The law of conservation of internal energy is a consequence of Newton's laws for stable, closed systems in which only conservative forces act. The total mechanical force of a closed system of material bodies, between which only thermal energy, remains constant.

Parallelogram rules in mechanics

Certain consequences follow from the three fundamental theories of Newton's body motion, one of which is addition total elements according to the parallelogram rule. According to this idea, the acceleration of any physical substance depends on the quantities that mainly characterize the action of other bodies, which determine the features of the process itself. Mechanical action on the object under study from the side external environment, which radically changes the speed of movement of several elements at once, is called force. It can be multifaceted.

In classical mechanics, which deals with speeds much less than the speed of light, mass is considered one of the main characteristics of the body itself, regardless of whether it is moving or at rest. The mass of a physical body is independent of the interaction of matter with other parts of the system.

Remark 1

Thus, mass gradually came to be understood as the amount of living matter.

The establishment of the concepts of mass and force, as well as the method for measuring them, allowed Newton to describe and formulate the second law of classical mechanics. So, mass is one of the key characteristics of matter, which determines its gravitational and inertial properties.

The first and second laws of mechanics refer, respectively, to the systematic motion of a single body or material point. In this case, only the action of other elements in a certain concept is taken into account. However, any physical action is an interaction.

The third law of mechanics already fixes this statement and says: an action always corresponds to an oppositely directed and equal reaction. In Newton's formulation, this postulate of mechanics is valid only for the case of a direct relationship of forces or in the case of a sudden transfer of the action of one material body to another. In the case of movement over a long period of time, the third law applies when the time of transfer of the action can be neglected.

In general, all the laws of classical mechanics are valid for the functioning of inertial frames of reference. In the case of non-inertial concepts, the situation is completely different. With accelerated movement of coordinates relative to the inertial frame itself, Newton's first law cannot be used - free bodies in it will change their speed of movement over time and depend on the speed of movement and energy of other substances.

Limits of applicability of the laws of classical mechanics

Figure 3. Limits of applicability of laws classical mechanics. Author24 - online exchange of student papers

As a result of the rather rapid development of physics at the beginning of the 20th century, a certain scope of application of classical mechanics was formed: its laws and postulates are valid for the motions of physical bodies, the speed of which is much less than the speed of light. It was determined that with increasing speed, the mass of any substance will automatically increase.

The discrepancy between the principles in classical mechanics mainly came from the fact that the future in in a certain sense is completely in the present - this determines the probability of accurately predicting the behavior of the system in any period of time.

Remark 2

The Newtonian method immediately became the main tool for understanding the essence of nature and all life on the planet. The laws of mechanics and methods of mathematical analysis soon showed their effectiveness and significance. The physical experiment, which was based on measuring technology, provided scientists with unprecedented accuracy.

Physical knowledge increasingly became the central industrial technology, which stimulated general development other important natural sciences.

In physics, all previously isolated electricity, light, magnetism and heat became whole and united in the electromagnetic hypothesis. And although the nature of gravity itself remained uncertain, its effects could be calculated. The concept of Laplace's mechanistic determinism was approved and implemented, which proceeds from the possibility of accurately determining the behavior of bodies at any time, if the initial conditions are initially determined.

The structure of mechanics as a science seemed quite reliable and solid, and also practically complete. As a result, the impression was that the knowledge of physics and its laws is close to its finale - such a powerful force was shown by the foundation of classical physics.

The emergence of classical mechanics was the beginning of the transformation of physics into a rigorous science, that is, a system of knowledge that affirms the truth, objectivity, validity and verifiability of both its initial principles and its final conclusions. This occurrence took place in the XVI-XVII centuries and is associated with the names Galileo Galilei, Rene Descartes and Isaac Newton. It was they who carried out the "mathematization" of nature and laid the foundations for an experimental-mathematical view of nature. They presented nature as a set of "material" points that have spatial-geometric (shape), quantitative-mathematical (number, magnitude) and mechanical (movement) properties and related cause-and-effect relationships that can be expressed in mathematical equations.

The beginning of the transformation of physics into a rigorous science was laid by G. Galileo. Galileo formulated a number of fundamental principles and laws of mechanics. Namely:

- principle of inertia, according to which, when a body moves along a horizontal plane without encountering any resistance to movement, then its movement is uniform and would continue constantly if the plane extended in space without end;

- principle of relativity, according to which in inertial systems all the laws of mechanics are the same and it is not possible, being inside, to determine whether it moves in a straight line and uniformly or is at rest;

- speed conservation principle and preservation of spatial and temporal intervals during the transition from one inertial system to another. It's famous Galilean transformation.

A holistic view of the logical-mathematical organized system basic concepts, principles and laws of mechanics received in the works of Isaac Newton. First of all, in the work "Mathematical Principles of Natural Philosophy" In this work, Newton introduces the concepts: weight, or the amount of matter, inertia, or the property of a body to resist a change in state of rest or motion, weight, as a measure of mass, force, or an action performed on a body to change its state.

Newton distinguished between absolute (true, mathematical) space and time, which do not depend on the bodies in them and are always equal to themselves, and relative space and time - moving parts of space and measurable durations of time.

A special place in Newton's concept is occupied by the doctrine of gravity or gravity, in which he combines the movement of "heavenly" and earthly bodies. This teaching includes the statements:

The gravity of a body is proportional to the amount of matter or mass contained in it;

Gravity is proportional to mass;

Gravity or gravity and there is that force which acts between the earth and the moon in inverse proportion to the square of the distance between them;

This gravitational force acts between all material bodies at a distance.

Regarding the nature of the force of gravity, Newton said: "I do not invent hypotheses."

The mechanics of Galileo-Newton, developed in the works of D. Alambert, Lagrange, Laplace, Hamilton ... eventually received a harmonious form that determined the physical picture of the world of that time. This picture was based on the principles of self-identity of the physical body; its independence from space and time; determinism, that is, a strict unambiguous cause-and-effect relationship between specific states of physical bodies; reversibility of all physical processes.

Thermodynamics.

Studies of the process of converting heat into work and vice versa, carried out in the 19th century by S. Kalno, R. Mayer, D. Joule, G. Hemholtz, R. Clausius, W. Thomson (Lord Kelvin), led to the conclusions about which R. Mayer wrote: "Motion, heat ..., electricity are phenomena that are measured by each other and pass into each other according to certain laws." Gemholtz generalizes Mayer's statement into the conclusion: "The sum of the tense and living forces existing in nature is constant." William Thomson refined the concepts of "intense and live forces" to the concepts of potential and kinetic energy, defining energy as the ability to do work. R. Clausius summarized these ideas in the formulation: "The energy of the world is constant." Thus, by the joint efforts of the community of physicists, a fundamental for all physical knowledge of the law of conservation and transformation of energy.

Studies of the processes of conservation and transformation of energy led to the discovery of another law - entropy increase law. "The transition of heat from a colder body to a warmer one," wrote Clausius, "cannot take place without compensation." The measure of the ability of heat to transform Clausius called entropy. The essence of entropy is expressed in the fact that in any isolated system, processes must proceed in the direction of converting all types of energy into heat while equalizing the temperature differences existing in the system. This means that real physical processes proceed irreversibly. The principle that asserts the tendency of entropy to a maximum is called the second law of thermodynamics. The first law is the law of conservation and transformation of energy.

The principle of increasing entropy posed a number of problems for physical thought: the relationship between the reversibility and irreversibility of physical processes, the formalities of the conservation of energy, which is not capable of doing work with the temperature homogeneity of bodies. All this required a deeper substantiation of the principles of thermodynamics. First of all, the nature of heat.

An attempt at such a justification was made by Ludwig Boltzmann, who, relying on the molecular-atomic concept of the nature of heat, came to the conclusion that statistical the nature of the second law of thermodynamics, since due to the huge number of molecules that make up macroscopic bodies, and the extreme speed and randomness of their movement, we observe only average values. Determination of average values is a problem of probability theory. At maximum temperature equilibrium, the chaos of molecular motion is also maximum, in which any order disappears. The question arises: can and, if so, how, out of chaos can order arise again? Physics will be able to answer this only in a hundred years, by introducing the principle of symmetry and the principle of synergy.

Electrodynamics.

By the middle of the 19th century, the physics of electrical and magnetic phenomena had reached a certain completion. A number of the most important laws of Coulomb, Ampère's law, the law of electromagnetic induction, the laws direct current etc. All these laws were based on long-range principle. The exception was the views of Faraday, who believed that electrical action is transmitted through a continuous medium, that is, on the basis of short range principle. Based on the ideas of Faraday, the English physicist J. Maxwell introduces the concept electromagnetic field and describes the state of matter "discovered" by him in his equations. "... The electromagnetic field, - Maxwell writes, - is that part of space that contains and surrounds bodies that are in an electrical or magnetic state." By combining the equations of the electromagnetic field, Maxwell obtains the wave equation, which implies the existence electromagnetic waves , whose propagation speed in air is equal to the speed of light. The existence of such electromagnetic waves was experimentally confirmed by the German physicist Heinrich Hertz in 1888.

In order to explain the interaction of electromagnetic waves with matter, the German physicist Hendrik Anton Lorenz put forward a hypothesis about the existence electron, that is, a small electrically charged particle, which is present in huge quantities in all weighty bodies. This hypothesis explained the phenomenon of splitting of spectral lines in a magnetic field discovered in 1896 by the German physicist Zeeman. In 1897, Thomson experimentally confirmed the presence of the smallest negatively charged particle or electron.

So, within the framework of classical physics, a rather harmonious and complete picture of the world arose, describing and explaining motion, gravity, heat, electricity and magnetism, and light. This gave Lord Kelvin (Thomson) a reason to say that the building of physics is practically built, only a few details are missing...

First, it turned out that Maxwell's equations are non-invariant under Galilean transformations. Secondly, the theory of aether, as an absolute coordinate system, to which Maxwell's equations are "attached", has not found experimental confirmation. Michelson-Morley experiment showed that there is no dependence of the speed of light on direction in a moving coordinate system No. Hendrik Lorentz, a supporter of the preservation of Maxwell's equations, having "attached" these equations to the ether as an absolute frame of reference, sacrificed Galileo's principle of relativity, its transformations and formulated his own transformations. It followed from G. Lorentz's transformations that spatial and temporal intervals are non-invariant in the transition from one inertial frame of reference to another. Everything would be fine, but the existence of an absolute medium - the ether, was not confirmed, as noted, experimentally. This is a crisis.

non-classical physics. Special theory of relativity.

Describing the logic of the creation of the special theory of relativity, Albert Einstein writes in a joint book with L. Infeld: “Now let us put together those facts that have been sufficiently verified by experience, without worrying more about the problem of the ether:

1. The speed of light in empty space is always constant, regardless of the movement of the light source or receiver.

2. In two coordinate systems moving rectilinearly and uniformly relative to each other, all the laws of nature are strictly the same, and there is no means of detecting absolute rectilinear and uniform motion ...

The first position expresses the constancy of the speed of light, the second generalizes Galileo's principle of relativity, formulated for mechanical phenomena, to everything that happens in nature. "Einstein notes that the acceptance of these two principles and the rejection of the principle of the Galilean transformation, since it contradicts the constancy of the speed of light, and put the beginning of the special theory of relativity.To the accepted two principles: the constancy of the speed of light and the equivalence of all inertial frames of reference, Einstein adds the principle of invariance of all laws of nature with respect to the transformations of G. Lorentz.Therefore, the same laws are valid in all inertial frames, and the transition from one system to another is given by Lorentz transformations, which means that the rhythm of a moving clock and the length of the moving rods depends on the speed: the rod will shrink to zero if its speed reaches the speed of light, and the rhythm of the moving clock slows down, the clock would stop completely if it could move at the speed of light.

Thus, Newtonian absolute time, space, motion, which were, as it were, independent of moving bodies and their state, were eliminated from physics.

General theory of relativity.

In the book already cited, Einstein asks: "Can we formulate physical laws in such a way that they are valid for all coordinate systems, not only for systems moving rectilinearly and uniformly, but also for systems moving completely arbitrarily with respect to each other?" . And he answers: "It turns out to be possible."

Having lost their "independence" from moving bodies and from each other in the special theory of relativity, space and time, as it were, "found" each other in a single space-time four-dimensional continuum. The author of the continuum, the mathematician Herman Minkowski, published in 1908 the work "Foundations of the Theory of Electromagnetic Processes", in which he argued that henceforth space itself and time itself should be reduced to the role of shadows, and only some kind of connection of both should still preserve independence. A. Einstein's idea was to represent all physical laws as properties this continuum as it metric. From this new position, Einstein considered Newton's law of gravity. Instead of gravitational force he started operating gravitational field. Gravitational fields were included in the space-time continuum as its "curvature". The continuum metric became a non-Euclidean, "Riemannian" metric. The "curvature" of the continuum began to be regarded as the result of the distribution of masses moving in it. The new theory explained the trajectory of Mercury's rotation around the Sun, which is not consistent with the Newtonian law of gravity, as well as the deflection of a beam of starlight passing near the Sun.

Thus, the concept of "inertial coordinate system" was eliminated from physics and the statement of the generalized principle of relativity: any coordinate system is equally suitable for describing natural phenomena.

Quantum mechanics.

The second, according to Lord Kelvin (Thomson), the missing element to complete the building of physics at the turn of the 19th-20th centuries was a serious discrepancy between theory and experiment in the study of laws thermal radiation absolutely black body. According to the prevailing theory, it must be continuous, continuous. However, this led to paradoxical conclusions, such as the fact that the total energy radiated by a black body at a given temperature is equal to infinity (the Rayleigh-Gene formula). To solve the problem, the German physicist Max Planck put forward the hypothesis in 1900 that matter cannot emit or absorb energy except in finite portions (quanta) proportional to the emitted (or absorbed) frequency. The energy of one portion (quantum) E=hn, where n is the radiation frequency, and h is a universal constant. Planck's hypothesis was used by Einstein to explain the photoelectric effect. Einstein introduced the concept of light quantum or photon. He also suggested that light, according to Planck's formula, has both wave and quantum properties. In the community of physicists, they started talking about wave-particle duality, especially since in 1923 another phenomenon was discovered confirming the existence of photons - the Compton effect.

In 1924, Louis de Broglie extended the idea of the dual corpuscular-wave nature of light to all particles of matter, introducing the concept of waves of matter. Hence, one can also speak about the wave properties of the electron, for example, about the diffraction of the electron, which were experimentally established. However, R. Feynman's experiments with electrons "bombarding" a shield with two holes showed that it is impossible, on the one hand, to say through which hole an electron flies, that is, to accurately determine its coordinate, and on the other hand, not to distort the pattern of distribution of registered electrons, without violating the nature of the interference. This means that we can know either the position of the electron or the momentum, but not both.

This experiment called into question the very concept of a particle in the classical sense of precise localization in space and time.

The explanation of the "non-classical" behavior of microparticles was first given by the German physicist Werner Heisenberg. The latter formulated the law of motion of a microparticle, according to which the knowledge of the exact coordinate of the particle leads to the complete uncertainty of its momentum, and vice versa, the exact knowledge of the particle's momentum leads to the complete uncertainty of its coordinates. W. Heisenberg established the ratio of uncertainties in the values of the coordinate and momentum of a microparticle:

Dx * DP x ³ h, where Dx is the uncertainty in the value of the coordinate; DP x - uncertainty in the value of the impulse; h is Planck's constant. This law and the uncertainty relation is called uncertainty principle Heisenberg.

Analyzing the uncertainty principle, the Danish physicist Niels Bohr showed that, depending on the setting of the experiment, a microparticle reveals either its corpuscular nature or a wave nature. but not both at once. Consequently, these two natures of microparticles mutually exclude each other, and at the same time should be considered as complementary, and their description based on two classes of experimental situations (corpuscular and wave) - an integral description of the microparticle. There is not a particle "in itself", but a system "particle - device". These conclusions of N. Bora were called principle of complementarity.

In the framework of this approach, uncertainty and complementarity turn out to be not a measure of our ignorance, but objective properties of microparticles, the microcosm as a whole. From this it follows that the statistical, probabilistic laws lie in the depths of physical reality, and the dynamic laws of unambiguous causal dependence are just some particular and idealized case of expressing statistical regularities.

Relativistic quantum mechanics.

In 1927, the English physicist Paul Dirac drew attention to the fact that to describe the movement of microparticles discovered by that time: electron, proton and photon, since they move at speeds close to the speed of light, the application of special relativity is required. Dirac compiled an equation that described the motion of an electron, taking into account the laws and quantum mechanics, and Einstein's theory of relativity. This equation was satisfied by two solutions: one solution gave a known electron with positive energy, the other - an unknown twin electron, but with negative energy. This is how the concept of particles and antiparticles symmetric to them arose. This gave rise to the question: is the vacuum empty? After Einstein's "expulsion" of the ether, it seemed undoubtedly empty.

Modern, well-proven ideas say that the vacuum is "empty" only on the average. It is constantly born and disappears great amount virtual particles and antiparticles. This does not contradict the uncertainty principle, which also has the expression DE * Dt ³ h. Vacuum in quantum theory field is defined as the lowest energy state of a quantum field, the energy of which is zero only on average. So vacuum is "something" called "nothing".

On the way to building a unified field theory.

In 1918, Emmy Noether proved that if a system is invariant under some global transformation, then there is a certain conservation value for it. It follows from this that the law of conservation (of energy) is a consequence of symmetries existing in real space-time.

Symmetry as a philosophical concept means the process of existence and formation of identical moments between different and opposite states of world phenomena. This means that, when studying the symmetry of any systems, it is necessary to consider their behavior under various transformations and to single out in the entire set of transformations those that leave immutable, invariant some functions corresponding to the considered systems.

IN modern physics the concept is used gauge symmetry. Railway workers understand the transition from a narrow gauge to a wide one by calibration. In physics, calibration was also originally understood as a change in level or scale. In special relativity, the laws of physics do not change with respect to translation or shift when calibrating distance. In gauge symmetry, the requirement of invariance gives rise to a certain specific type of interaction. Therefore, the gauge invariance allows answering the question: "Why and why do such interactions exist in nature?". At present, the existence of four types is determined in physics physical interactions: gravitational, strong, electromagnetic and weak. All of them have a gauge nature and are described by gauge symmetries, which are different representations of Lie groups. This suggests the existence of a primary supersymmetric field, which does not yet distinguish between types of interactions. Differences, types of interaction are the result of spontaneous, spontaneous violation of the symmetry of the original vacuum. The evolution of the universe appears then as synergistic self-organizing process: in the process of expansion from the vacuum supersymmetric state, the Universe warmed up to the "big bang". The further course of its history ran through critical points - bifurcation points, in which spontaneous violations of the symmetry of the initial vacuum occurred. Statement self-organization systems through spontaneous breaking of the original type of symmetry at bifurcation points and eat synergy principle.

The choice of the direction of self-organization at bifurcation points, that is, at points of spontaneous violation of the initial symmetry, is not accidental. It is defined as if already present at the level of vacuum supersymmetry by the "project" of a person, that is, the "project" of a creature asking why the world is like this. This anthropic principle, which was formulated in physics in 1962 by D. Dicke.

The principles of relativity, uncertainty, complementarity, symmetry, synergy, the anthropic principle, as well as the assertion of the deep-basic nature of probabilistic causal dependencies in relation to dynamic, unambiguous causal dependencies, constitute the categorical-conceptual structure of the modern gestalt, the image of physical reality.

Literature

1. Akhiezer A.I., Rekalo M.P. Modern physical picture of the world. M., 1980.

2. Bohr N. Atomic physics and human knowledge. M., 1961.

3. Bor N. Causality and complementarity// Bor N. Selected scientific works in 2 vols. V.2. M., 1971.

4. Born M. Physics in the life of my generation, M., 1061.

5. Broglie L. De. Revolution in physics. M., 1963

6. Heisenberg V. Physics and Philosophy. Part and whole. M. 1989.

8. Einstein A., Infeld L. The evolution of physics. M., 1965.

Mechanics is a branch of physics that studies one of the simplest and most general forms of motion in nature, called mechanical motion.

mechanical movement consists in changing the position of bodies or their parts relative to each other over time. So mechanical movement is made by planets circulating in closed orbits around the Sun; various bodies moving on the surface of the Earth; electrons moving under the influence of an electromagnetic field, etc. Mechanical movement is present in other more complex forms matter as an integral but not exhaustive part.

Depending on the nature of the objects being studied, mechanics is subdivided into the mechanics of a material point, the mechanics of a solid body, and the mechanics of a continuum.

The principles of mechanics were first formulated by I. Newton (1687) on the basis of an experimental study of the motion of macrobodies with small velocities compared to the speed of light in vacuum (3·10 8 m/s).

macrobodies called ordinary bodies that surround us, that is, bodies consisting of a huge number of molecules and atoms.

The mechanics that studies the motion of macrobodies with velocities much lower than the speed of light in vacuum is called classical.

Classical mechanics is based on the following Newton's ideas about the properties of space and time.

Any physical process proceeds in space and time. This can be seen at least from the fact that in all areas of physical phenomena, each law explicitly or implicitly contains space-time quantities - distances and time intervals.

A space that has three dimensions obeys Euclidean geometry, that is, it is flat.

Distances are measured by scales, the main property of which is that two scales that once coincided in length always remain equal to each other, that is, they coincide with each subsequent overlay.

Time intervals are measured by hours, and the role of the latter can be played by any system that performs a repeating process.

The main feature of the ideas of classical mechanics about the size of bodies and time intervals is their absoluteness: the scale always has the same length, no matter how it moves relative to the observer; two clocks having the same rate and once brought into line with each other show the same time, no matter how they move.

Space and time have remarkable properties symmetry that impose restrictions on the flow of certain processes in them. These properties have been established by experience and seem so obvious at first glance that there seems to be no need to single them out and deal with them. Meanwhile, if there were no spatial and temporal symmetry, no physical science could neither arise nor develop.

It turns out that the space uniformly And isotropically, and the time is uniformly.

The homogeneity of space lies in the fact that the same physical phenomena under the same conditions are carried out in the same way various parts space. All points of space, therefore, are completely indistinguishable, equal in rights, and any of them can be taken as the origin of the coordinate system. The homogeneity of space is manifested in the law of conservation of momentum.

Space also has isotropy: the same properties in all directions. The isotropy of space is manifested in the law of conservation of angular momentum.

The homogeneity of time lies in the fact that all moments of time are also equal, equivalent, that is, the course of identical phenomena in the same conditions is the same, regardless of the time of their implementation and observation.

The homogeneity of time is manifested in the law of conservation of energy.

Were it not for these homogeneity properties, installed in Minsk physical law would be unfair in Moscow, and open today in the same place could be unfair tomorrow.

In classical mechanics, the validity of the Galileo-Newton law of inertia is recognized, according to which a body that is not subject to action from other bodies moves in a straight line and uniformly. This law asserts the existence of inertial frames of reference in which Newton's laws (as well as Galileo's principle of relativity) hold. Galileo's principle of relativity states, that all inertial frames of reference are mechanically equivalent to each other, all the laws of mechanics are the same in these frames of reference, or, in other words, they are invariant with respect to the Galilean transformations expressing the space-time connection of any event in different inertial frames of reference. Galilean transformations show that the coordinates of any event are relative, that is, they have different meanings V different systems reference; the instants of time when the event occurred are the same in different systems. The latter means that time flows in the same way in different frames of reference. This circumstance seemed so obvious that it was not even mentioned as a special postulate.

In classical mechanics, the principle of long-range action is observed: the interactions of bodies propagate instantly, that is, at an infinitely high speed.

Depending on the speed with which bodies move and what are the sizes of the bodies themselves, mechanics is divided into classical, relativistic, and quantum.

As already mentioned, laws classical mechanics are applicable only to the motion of macrobodies, the mass of which is much greater than the mass of an atom, at low speeds compared to the speed of light in vacuum.

Relativistic mechanics considers the motion of macrobodies with velocities close to the speed of light in vacuum.

Quantum mechanics- mechanics of microparticles moving at speeds much lower than the speed of light in vacuum.

Relativistic quantum mechanics - the mechanics of microparticles moving at speeds approaching the speed of light in a vacuum.

To determine whether a particle belongs to macroscopic ones, whether classical formulas are applicable to it, one must use Heisenberg's uncertainty principle. According to quantum mechanics, real particles can only be characterized in terms of position and momentum with some accuracy. The limit of this accuracy is defined as follows

Where
ΔX - coordinate uncertainty;
ΔP x - uncertainty of the projection on the momentum axis;
h - Planck's constant, equal to 1.05·10 -34 J·s;
"≥" - more than a value, of the order of ...

Replacing momentum with the product of mass times velocity, we can write

It can be seen from the formula that the smaller the mass of a particle, the less certain its coordinates and speed become. For macroscopic bodies practical applicability classic way description of the movement is not in doubt. Suppose, for example, that we are talking about the motion of a ball with a mass of 1 g. Usually, the position of the ball can practically be determined with an accuracy of a tenth or a hundredth of a millimeter. In any case, it hardly makes sense to talk about an error in determining the position of the ball, which is smaller than the dimensions of the atom. Let us therefore ΔX=10 -10 m. Then from the uncertainty relation we find

The simultaneous smallness of the values ΔX and ΔV x is the proof of the practical applicability of the classical method of describing the motion of macrobodies.

Consider the motion of an electron in a hydrogen atom. The mass of an electron is 9.1 10 -31 kg. The error in the position of the electron ΔX in any case should not exceed the dimensions of the atom, that is, ΔX<10 -10 м. Но тогда из соотношения неопределенностей получаем

This value is even greater than the speed of an electron in an atom, which is equal in order of magnitude to 10 6 m/s. In this situation, the classical picture of movement loses all meaning.

Mechanics are divided into kinematics, statics and dynamics. Kinematics describes the movement of bodies without being interested in the causes that caused this movement; statics considers the conditions for the equilibrium of bodies; dynamics studies the movement of bodies in connection with those causes (interactions between bodies) that determine one or another character of movement.

The real movements of bodies are so complex that, while studying them, it is necessary to abstract from the details that are not essential for the movement under consideration (otherwise the problem would become so complicated that it would be practically impossible to solve it). For this purpose, concepts (abstractions, idealizations) are used, the applicability of which depends on the specific nature of the problem of interest to us, as well as on the degree of accuracy with which we want to obtain the result. Among these concepts, the most important are the concepts material point, system of material points, absolutely rigid body.

A material point is a physical concept that describes the translational motion of a body, if only its linear dimensions are small in comparison with the linear dimensions of other bodies within the given accuracy of determining the body coordinate, moreover, the mass of the body is attributed to it.

In nature, material points do not exist. One and the same body, depending on the conditions, can be considered either as a material point or as a body of finite dimensions. Thus, the Earth moving around the Sun can be considered a material point. But when studying the rotation of the Earth around its axis, it can no longer be considered a material point, since the nature of this movement is significantly influenced by the shape and size of the Earth, and the path traveled by any point on the earth's surface in a time equal to the period of its revolution around its axis, we compare with the linear dimensions of the globe. An aircraft can be considered as a material point if we study the movement of its center of mass. But if it is necessary to take into account the influence of the environment or determine the forces in individual parts of the aircraft, then we must consider the aircraft as an absolutely rigid body.

An absolutely rigid body is a body whose deformations can be neglected under the conditions of a given problem.

The system of material points is a set of bodies under consideration, which are material points.

The study of the motion of an arbitrary system of bodies is reduced to the study of a system of interacting material points. It is natural, therefore, to begin the study of classical mechanics with the mechanics of one material point, and then proceed to the study of a system of material points.

Fundamentals of classical mechanics

Mechanics- a branch of physics that studies the laws of mechanical motion of bodies.

Body- material object.

mechanical movement- change provisions body or its parts in space over time.

Aristotle imagined this type of movement as a direct change by the body of its place relative to other bodies, since in his physics the material world was inextricably linked with space, existed together with it. Time he considered a measure of the movement of the body. Later changes in views on the nature of motion led to the gradual separation of space and time from physical bodies. Finally, absolutization space and time by Newton generally led them beyond the limits of possible experience.

However, this approach made it possible by the end of the 18th century to build a complete system mechanics, now called classical. classic is that she:

1) describes the majority of mechanical phenomena in the macroworld, using a small number of initial definitions and axioms;

2) strictly justified mathematically;

3) is often used in more specific areas of science.

Experience shows that classical mechanics is applicable to the description of the motion of bodies with velocities υ<< с ≈ 3·10 8 м/с. Ее основные разделы:

1) statics studies the conditions for the equilibrium of bodies;

2) kinematics - the movement of bodies without taking into account its causes;

3) dynamics - the influence of the interaction of bodies on their movement.

Main concepts of mechanics:

1) A mechanical system is a mentally selected set of bodies that are essential in a given task.

2) A material point is a body whose shape and dimensions can be neglected within the framework of this task. The body can be represented as a system of material points.

3) An absolutely rigid body is a body, the distance between any two points of which does not change under the conditions of a given problem.

4) The relativity of motion lies in the fact that a change in the position of a body in space can only be established in relation to some other bodies.

5) Reference body (RT) is an absolutely rigid body, relative to which the motion is considered in this problem.

6) Reference system (SO) = (TO + SC + hours). The origin of the coordinate system (SC) is aligned with some TO point. Clocks measure periods of time.

Cartesian SC:

Figure 5

Position material point M is described radius-vector of a point, are its projections on the coordinate axes.

If we set the initial time t 0 = 0, then the movement of the point M will be described vector function or three scalar functions x(t),y(t), z(t).

Linear characteristics of the movement of a material point:

1) trajectory - the line of motion of a material point (geometric curve),

2) path ( S) is the distance traveled along it in the time interval ,

3) moving,

4) speed,

5) acceleration.

Any movement of a rigid body can be reduced to two main types - progressive And rotational around a fixed axis.

translational movement- such that the line connecting any two points of the body remains parallel to its original position. Then all points move in the same way, and the motion of the whole body can be described one point movement.

Rotation around a fixed axis - such a movement in which there is a straight line, rigidly connected with the body, all points of which remain fixed in a given FR. The trajectories of the remaining points are circles centered on this line. In this case, convenient angular characteristics movements that are the same for all points of the body.

Angular characteristics of motion of a material point:

1) angle of rotation (angular path), measured in radians [rad], where r is the radius of the point trajectory,

2) angular displacement, the module of which is the angle of rotation in a small period of time dt,

3) angular velocity,

4) angular acceleration.

Figure 6

Relationship between angular and linear characteristics:

Dynamics uses power concept, measured in newtons (H), as a measure of the impact of one body on another. This impact is the cause of the movement.

The principle of superposition of forces- the resulting effect of the impact on the body of several bodies is equal to the sum of the effects of the impacts of each of these bodies separately. The value is called the resultant force and characterizes the equivalent effect on the body n tel.

Newton's laws summarize the experimental facts of mechanics.

Newton's 1st law. There are reference systems, relative to which a material point maintains a state of rest or uniform rectilinear motion in the absence of a force effect on it, i.e. if , then .

Such a motion is called inertial motion or inertial motion, and therefore frames of reference in which Newton's 1st law holds are called inertial(ISO).

Newton's 2nd law. , where is the momentum of the material point, m is its mass, i.e. if , then and, therefore, the motion will no longer be inertial.

Newton's 3rd law. When two material points interact, forces arise and are applied to both points, and .

Mechanics is the study of the balance and movement of bodies (or their parts) in space and time. Mechanical motion is the simplest and at the same time (for humans) the most common form of the existence of matter. Therefore, mechanics occupies an exceptionally important place in natural science and is the main subsection of physics. It historically arose and formed as a science earlier than other subsections of natural science.

Mechanics includes statics, kinematics and dynamics. In statics, the conditions for the equilibrium of bodies are studied, in kinematics - the movements of bodies from a geometric point of view, i.e. without taking into account the action of forces, but in dynamics - taking into account these forces. Statics and kinematics are often regarded as an introduction to dynamics, although they also have independent significance.

Until now, by mechanics we have meant classical mechanics, the construction of which was completed by the beginning of the 20th century. Within the framework of modern physics, there are two more mechanics - quantum and relativistic. But in more detail we will consider classical mechanics.

Classical mechanics considers the motion of bodies with velocities much less than the speed of light. According to the special theory of relativity, for bodies moving at high speeds close to the speed of light, there is no absolute time and absolute space. Hence, the nature of the interaction of bodies becomes more complicated, in particular, the mass of the body, it turns out, depends on the speed of its movement. All this was the subject of consideration of relativistic mechanics, for which the constant of the speed of light plays a fundamental role.

Classical mechanics is based on the following fundamental laws.

Galileo's principle of relativity

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. 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 three laws are the basis of classical mechanics.

1. Any material body maintains a state of rest or uniform rectilinear motion until the impact from other bodies makes it change this state. The desire of the body to maintain a state of rest or uniform rectilinear motion is called inertia. Therefore, the first law is also called the law of inertia.
2. The acceleration acquired by the body is directly proportional to the force acting on the body, and inversely proportional to the mass of the body.
3. The forces with which interacting bodies act on each other are equal in magnitude and opposite in direction.

We know Newton's second law in the form

natural science classic mechanics law

F \u003d m H a, or a \u003d F / m,

where the acceleration a received by the body under the action of the force F is inversely proportional to the mass of the body m.

The first law can be obtained from the second, since in the absence of other forces acting on the body, the acceleration is also zero. However, the first law is considered as an independent law, since it states the existence of inertial frames of reference. In mathematical formulation, Newton's second law is most often written in the following form:

where is the resulting vector of forces acting on the body; -- body acceleration vector; m -- body weight.

Newton's third law specifies some properties of the concept of force introduced in the second law. He postulates the presence for each force acting on the first body from the second, equal in magnitude and opposite in direction of the force acting on the second body from the first. The presence of Newton's third law ensures the fulfillment of the law of conservation of momentum for a system of bodies.

Law of conservation of momentum

This law is a consequence of Newton's laws for closed systems, that is, systems that are not affected by external forces or the actions of external forces are compensated and the resulting force is zero. From a more fundamental point of view, there is a relationship between the law of conservation of momentum and the homogeneity of space, expressed by Noether's theorem.

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. The energy given by one body to another is always equal to the energy received by the other body. To quantify the process of energy exchange between interacting bodies in mechanics, the concept of the work of a force that causes motion is introduced. The force that causes the body to move does work, and the energy of the moving body increases by the amount of work expended. As you know, a body of mass m moving at a speed v has a kinetic energy

Potential energy is the mechanical energy of a system of bodies that interact through force fields, for example, through gravitational forces. The work done by these forces when moving a body from one position to another does not depend on the trajectory of motion, but depends only on the initial and final positions of the body in the force field. Gravitational forces are conservative forces, and the potential energy of a body of mass m raised to a height h above the Earth's surface is equal to

E sweat = mgh,

where g is the free fall acceleration.

The total mechanical energy is equal to the sum of the kinetic and potential energy.