Which was the main classical mechanics. Principles of classical mechanics. Modern development of 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 relies 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 in general form formulated the equations of the theory of elasticity. 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 quantum field theory is used instead of classical mechanics. For systems with a very large number of 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 of 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 the 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 entropy, and to the ultraviolet catastrophe, in which a 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

Sir ISAAC NEWTON (January 4, 1643 - March 31, 1727) - an outstanding English scientist who laid the foundations of modern natural science, the creator of classical physics, a member of the Royal Society of London and its president (since 1703). Born in Woolsthorpe. Graduated from Cambridge University in 1665. In March-June 1666, Newton visited Cambridge. However, in the summer, a new wave of plague forced him to leave home again. Finally, in early 1667, the epidemic subsided, and in April Newton returned to Cambridge. On October 1, he was elected a Fellow of Trinity College, and in 1668 became a master. He was given a spacious private room to live in, a salary of £2 a year, and a group of students with whom he conscientiously studied standard subjects for several hours a week. However, neither then nor later did Newton become famous as a teacher, his lectures were poorly attended. one

Having consolidated his position, Newton traveled to London, where shortly before, in 1660, the Royal Society of London was established - an authoritative organization of prominent scientists, one of the first Academies of Sciences. The printed organ of the Royal Society was the journal Philosophical Transactions.

In 1669, mathematical works began to appear in Europe using expansions into infinite series. Although the depth of these discoveries was no match for Newton's, Barrow insisted that his student fix his priority in this matter. 2 ______________________________

1. https://ru.wikipedia.org/

2. Akroyd P. “Isaac Newton. Biography". - M.: Hummingbird, Azbuka-Atticus, 2011

Newton wrote a brief but fairly complete summary of this part of his discoveries, which he called "Analysis by means of equations with an infinite number of terms." Barrow sent this treatise to London. Newton asked Barrow not to reveal the name of the author of the work (but he still let it slip). "Analysis" spread among specialists and gained some notoriety in England and beyond.

In the same year, Barrow accepted the invitation of the king to become a court chaplain and left teaching. On October 29, 1669, the 26-year-old Newton was elected as his successor, professor of mathematics and optics at Trinity College, with a high salary of £100 a year. Barrow left Newton an extensive alchemical laboratory; during this period, Newton became seriously interested in alchemy, conducted a lot of chemical experiments. Newton formulated the basic laws of classical mechanics, discovered the law of universal gravitation, the dispersion of light, developed the corpuscular theory of light, and developed differential and integral calculus. Summarizing the results of the research of his predecessors in the field of mechanics and his own, Newton created a huge work "Mathematical Principles of Natural Philosophy" ("Beginnings"), published in 1687. "Beginnings" contained the basic concepts of classical mechanics, in particular the concepts: mass, momentum, force, acceleration, centripetal force and three laws of motion. In the same work, his law of universal gravitation is given, on the basis of which Newton explained the motion of celestial bodies and created the theory of gravitation. 1 The discovery of this law finally confirmed the victory of the teachings of Copernicus. He showed that Kepler's three laws follow from the law of universal gravitation; explained the features of the movement of the moon, the phenomenon of the procession; developed the theory of the figure of the Earth, noting that it should be compressed at the poles, _____________________________

1. Akroyd P. “Isaac Newton. Biography". - M.: Hummingbird, Azbuka-Atticus, 2011

the theory of ebbs and flows; considered the problem of creating an artificial satellite of the Earth, etc. Newton developed the law of resistance and the basic law internal friction in liquids and gases, gave a formula for the speed of wave propagation.

At the turn of the XIX-XX centuries. the limits of applicability of classical mechanics were identified (see the section "Limitations of applicability of classical mechanics" at the end of the article). It turned out that it gives exceptionally accurate results, but only in those cases when it is applied 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, and at distances or conditions when the speed of propagation of gravity can be considered infinite ( 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 relativistic effects are considered by quantum field theory).

Nevertheless, classical mechanics retains its value because it:

Much easier to understand and use than other theories.
In an extensive range, it describes reality quite well.

Classical mechanics can be used to describe the motion of a very wide class of physical objects: both ordinary objects in the macrocosm (such as a spinning top and a baseball), and objects of astronomical dimensions (such as planets and stars), and many microscopic objects.

Encyclopedic YouTube

1 / 5

✪ Lecture 1. | 8.01 Physics I: Classical mechanics, autumn 1999

✪ Quantum mechanics 1 - Failure of classical physics

✪ Physics - Newton's first and second laws

✪ Mechanics - Basic concepts of mechanics

✪ Mechanics. Newton's laws. Forces

Subtitles

Basic concepts

Classical mechanics operates with several basic concepts and models. Among them should be highlighted:

Space . It is believed that the movement of bodies occurs in space, which is Euclidean, absolute (does not depend on the observer), homogeneous (any two points in space are indistinguishable) and isotropic (any two directions in space are indistinguishable).
Time is a fundamental concept postulated in classical mechanics. It is believed that time is absolute, homogeneous and isotropic (the equations of classical mechanics do not depend on the direction of the flow of time).
The reference system consists of a reference body (some body, real or imaginary, relative to which the movement of a mechanical system is considered), a device for measuring time and a coordinate system.
Mass is a measure of the inertia of bodies.
A material point is a model of an object that has a mass, the dimensions of which are neglected in the problem being solved. Bodies of non-zero size can experience complex motions because their internal configuration can change (for example, the body can rotate or deform). Nevertheless, in certain cases, the results obtained for material points are applicable to such bodies, if we consider such bodies as aggregates of a large number of interacting material points. Material points in kinematics and dynamics are usually described by the following quantities:
- Radius vector r → (\displaystyle (\vec (r)))- a vector drawn from the origin of coordinates to that point in space, which serves as the current position of the material point
- Velocity is a vector that characterizes the change in the position of a material point with time and is defined as the derivative of the radius vector with respect to time: v → = d r → d t (\displaystyle (\vec (v))=(\frac (d(\vec (r)))(dt)))
- Acceleration is a vector that characterizes the change in the speed of a material point with time and is defined as the derivative of speed with respect to time: a → = dv → dt = d 2 r → dt 2 (\displaystyle (\vec (a))=(\frac (d(\vec (v)))(dt))=(\frac (d^(2 )(\vec (r)))(dt^(2))))
- Mass - a measure of the inertia of a material point; is assumed to be constant in time and independent of any features of the motion of a material point and its interaction with other bodies.
- Impulse (another name is the amount of motion) is a vector physical quantity equal to the product of the mass of a material point and its speed: p → = m v → . (\displaystyle (\vec (p))=m(\vec (v)).)
- Kinetic energy - the energy of motion of a material point, defined as half the product of the mass of the body and the square of its speed: T = m v 2 2 . (\displaystyle T=(\frac (mv^(2))(2)).) or T = p 2 2 m . (\displaystyle T=(\frac (p^(2))(2m)).)
- Force is a vector physical quantity, which is a measure of the intensity of the impact on a given body of other bodies, as well as physical fields. It is a function of the coordinates and velocity of a material point, which determines the time derivative of its momentum.
- If the work of the force does not depend on the type of trajectory along which the body moved, but is determined only by its initial and final positions, then such a force is called potential. The interaction that occurs through potential forces can be described by potential energy. By definition, potential energy is a function of body coordinates U (r →) (\displaystyle U((\vec (r)))) such that the force acting on the body is equal to the gradient from this function, taken with the opposite sign: F → = − ∇ U (r →) . (\displaystyle (\vec (F))=-\nabla U((\vec (r))).)

Basic Laws

Galileo's principle of relativity

The basic principle on which classical mechanics is based is the principle of relativity, formulated by G. Galileo on the basis of empirical observations. 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

The basis of classical mechanics is Newton's three laws (formulating these laws, Newton used the term "body", although in fact they are talking about material points).

Newton's second law is not enough to describe the motion of a particle. Additionally, a description of the force is required. F → (\displaystyle (\vec (F))), 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). The fundamental basis of this law is the property uniformity of time, and the relationship between the law of conservation of energy and this property is again expressed by Noether's theorem.

Spread to extended bodies

Classical mechanics also includes a description of the complex motions of extended non-point objects. The extension of the laws of Newtonian mechanics to such objects was largely due to Euler. The modern formulation of Euler's laws also uses the apparatus of three-dimensional vectors.

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 the contribution of the electromagnetic field to the momentum of the system is ignored; such a contribution is expressed in terms of the Poynting vector divided by c 2 , where c is the speed of light in free space.

Story

Antiquity

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 lever rule, the theorem on the addition of parallel forces, introduced the concept of the center of gravity, laid the foundations of hydrostatics (the force of Archimedes).

Middle Ages

new time

17th century

The laying of the foundations of classical mechanics was completed by the works of Isaac Newton, who formulated the laws of mechanics in the most general form and discovered the law of universal gravitation. In 1684, he also established a law viscous friction in liquids and gases.

Also in the 17th century, in 1660, the law of elastic deformations was formulated, bearing the name of its discoverer Robert Hooke.

18th century

19th century

Classical mechanics is a self-consistent theory, that is, within its framework there are no statements that contradict each other. In general, it is compatible with other "classical" theories (such as classical electrodynamics and classical thermodynamics), but in late XIX century revealed some inconsistencies between these theories; overcoming these discrepancies marked the formation of modern physics. In particular:

The equations of classical electrodynamics are non-invariant with respect to Galilean transformations: since these equations include (as a physical constant, constant for all observers) the speed of light , then classical electrodynamics and classical mechanics are compatible only in one chosen frame of reference - associated with the ether. But experimental verification did not reveal the existence of the ether, and this led to the creation of a special theory of relativity (under which the equations of mechanics were modified).
Some statements of classical thermodynamics are also incompatible with classical mechanics: their application together with the laws of classical mechanics leads to the Gibbs paradox (according to which it is impossible to accurately determine the value of entropy) and to the ultraviolet catastrophe (the latter means that

(January 4, 1643, Woolsthorpe, near Grantham, Lincolnshire, England - March 31, 1727, London) - English mathematician, mechanic, astronomer and physicist, creator of classical mechanics, member (1672) and president (since 1703) of the Royal Society of London.

One of the founders of modern physics, formulated the basic laws of mechanics and was the actual creator of a unified physical program for describing all physical phenomena based on mechanics; discovered the law of universal gravitation, explained the motion of the planets around the Sun and the Moon around the Earth, as well as the tides in the oceans, laid the foundations of continuum mechanics, acoustics and physical optics.

Childhood

Isaac Newton was born in a small village in the family of a small farmer who died three months before the birth of his son. The baby was premature; there is a legend that he was so small that he was placed in a sheepskin mitten lying on a bench, from which he once fell out and hit his head hard on the floor.

When the child was three years old, his mother remarried and left, leaving him in the care of his grandmother. Newton grew up sickly and unsociable, prone to daydreaming. He was attracted by poetry and painting, he, far from his peers, made kites, invented a windmill, a water clock, a pedal cart.

The beginning was difficult for Newton school life. He studied poorly, was a weak boy, and once classmates beat him until he lost consciousness. To endure such a humiliating situation was unbearable for the proud Newton, and there was only one thing left: to stand out with academic success. By hard work, he achieved the fact that he took first place in the class.

Interest in technology made Newton think about the phenomena of nature; he was also deeply involved in mathematics. Jean Baptiste Biot later wrote about this: “One of his uncles, finding him one day under a hedge with a book in his hands, immersed in deep reflection, took the book from him and found that he was busy solving a mathematical problem. Struck by such a serious and active direction of such a young man, he persuaded his mother not to resist further the desire of her son and send him to continue his studies. After serious training, Newton entered Cambridge in 1660 as a Subsizzfr`a (the so-called poor students who were obliged to serve the members of the college, which could not but burden Newton).

The beginning of creativity. Optics

In six years, Newton completed all the degrees of the college and prepared all his further great discoveries. In 1665 Newton became a master of arts.

In the same year, when the plague was raging in England, he decided to temporarily settle in Woolsthorpe. It was there that he began to actively engage in optics; The search for ways to eliminate chromatic aberration in lens telescopes led Newton to research what is now called dispersion, i.e., the dependence of the refractive index on frequency. Many of the experiments he conducted (and there are more than a thousand of them) have become classic and are repeated today in schools and institutes.

The leitmotif of all research was the desire to understand the physical nature of light. At first, Newton was inclined to think that light is waves in the all-penetrating ether, but later he abandoned this idea, deciding that the resistance from the ether should have noticeably slowed down the movement of celestial bodies. These arguments led Newton to the idea that light is a stream of special particles, corpuscles, emitted from a source and moving in a straight line until they encounter obstacles. The corpuscular model explained not only the straightness of light propagation, but also the law of reflection (elastic reflection), and - though not without an additional assumption - the law of refraction. This assumption consisted in the fact that light corpuscles, flying up to the surface of water, for example, should be attracted by it and therefore experience acceleration. According to this theory, the speed of light in water must be greater than in air (which conflicted with later experimental data).

Laws of mechanics

The formation of corpuscular ideas about light was clearly influenced by the fact that at that time the work that was destined to become the main great result of Newton's works was already completed - the creation of a single physical picture of the World based on the laws of mechanics formulated by him.

This picture was based on the idea of material points - physically infinitely small particles of matter and the laws governing their movement. It was precisely the precise formulation of these laws that gave Newton's mechanics completeness and completeness. The first of these laws was, in fact, the definition of inertial frames of reference: it is in such systems that material points that do not experience any influences move uniformly and rectilinearly. The second law of mechanics plays a central role. It says that the change in quantity, movement (the product of mass and speed) per unit of time is equal to the force acting on a material point. The mass of each of these points is a fixed quantity; in general, all these points "do not wear out", according to Newton, each of them is eternal, that is, it can neither arise nor be destroyed. Material points interact, and force is the quantitative measure of influence on each of them. The task of finding out what these forces are is the root problem of mechanics.

Finally, the third law - the law of "equality of action and reaction" explained why the total momentum of any body that does not experience external influences remains unchanged, no matter how its constituent parts interact with each other.

Law of gravity

Having posed the problem of studying various forces, Newton himself gave the first brilliant example of its solution by formulating the law of universal gravitation: the force of gravitational attraction between bodies whose dimensions are much smaller than the distance between them is directly proportional to their masses, inversely proportional to the square of the distance between them and directed along the connecting line. their straight line. The law of universal gravitation allowed Newton to give a quantitative explanation of the motion of the planets around the Sun and the Moon around the Earth, to understand the nature of sea tides. This could not but make a huge impression on the minds of researchers. The program of a unified mechanical description of all natural phenomena - both "terrestrial" and "heavenly" for many years was established in physics. Moreover, for two centuries many physicists considered the very question of the limits of applicability of Newton's laws to be unjustified.

In 1668 Newton returned to Cambridge and he soon received the Lucas Chair in Mathematics. Before him, this department was occupied by his teacher I. Barrow, who ceded the department to his beloved student in order to financially provide for him. By that time, Newton was already the author of the binomial and the creator (simultaneously with Leibniz, but independently of him) of the method of fluxions - what is now called differential and integral calculus. In general, that was the most fruitful period in Newton's work: in seven years, from 1660 to 1667, his main ideas were formed, including the idea of the law of universal gravitation. Not limited to theoretical studies alone, in the same years he designed and began to create a reflecting telescope (reflective). This work led to the discovery of what later became known as "lines of equal thickness" interference. (Newton, realizing that here the “quenching of light by light” is manifested, which did not fit into the corpuscular model, tried to overcome the difficulties that arose here by introducing the assumption that corpuscles in light move in waves - “tides”). The second of the manufactured telescopes (improved) was the reason for the presentation of Newton as a member of the Royal Society of London. When Newton refused membership, citing lack of funds to pay membership dues, it was considered possible, given his scientific merits, to make an exception for him, exempting him from paying them.

Being by nature a very cautious (not to say timid) person, Newton, against his will, sometimes found himself drawn into discussions and conflicts that were painful for him. Thus, his theory of light and colors, presented in 1675, caused such attacks that Newton decided not to publish anything on optics while he was alive. gook, his most bitter opponent. Newton had to take part in political events. From 1688 to 1694 he was a Member of Parliament. By that time, in 1687, his main work, The Mathematical Principles of Natural Philosophy, was published - the basis of the mechanics of all physical phenomena, from the movement of celestial bodies to the propagation of sound. For several centuries ahead, this program determined the development of physics, and its significance has not been exhausted to this day.

Newton's disease

Constant huge nervous and mental stress led to the fact that in 1692 Newton fell ill with a mental disorder. The immediate impetus for this was a fire in which all the manuscripts prepared by him perished. Only by 1694 he, according to the testimony Huygens, "... is already beginning to understand his book "Beginnings"".

The constant oppressive feeling of material insecurity was undoubtedly one of the causes of Newton's illness. Therefore, it was important for him to be the caretaker of the Mint with the preservation of a professorship at Cambridge. Zealously setting to work and quickly achieving notable success, he was appointed director in 1699. It was impossible to combine this with teaching, and Newton moved to London. At the end of 1703 he was elected President of the Royal Society. By that time, Newton had reached the pinnacle of fame. In 1705, he was elevated to the dignity of knighthood, but, having a large apartment, six servants and a rich departure, he remains still alone. The time for active creativity is over, and Newton is limited to preparing the publication of Optics, reprinting the Elements and interpreting the Holy Scriptures (he owns the interpretation of the Apocalypse, an essay on the prophet Daniel).

Newton was buried in Westminster Abbey. The inscription on his grave ends with the words: "Let mortals rejoice that such an adornment of the human race lived in their midst."

“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 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 crafts, 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 are studied, observed in nature and man-made during his activities.

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 significance for mankind 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 the consideration of geometric figures, said to a 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 off the face of the earth all the achievements of science and culture. 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 basic principles of the philosophy of Aristotle were considered a violation of the foundations of the Holy Scripture, and researchers who decided to do this were declared 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. Big number work on mechanics in the Middle Ages was devoted to finding " perpetuum mobile”, i.e. perpetual motion machine operating without receiving energy from outside. Most of these works contributed little to the development of mechanics (The ideology of the Middle Ages was well expressed by Mahomet, 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 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 natural movement of a falling body is an 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 refined by Galileo (as, for example, the law of 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 experiments, 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 a new force or obstacle?
Simplicio: I have no doubt that the same body in the same medium has a constant speed determined by nature, which cannot increase except by the application of a new force, or decrease except by 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 a large stone moves, say, with a speed of eight cubits, while another, smaller one, with a speed of four cubits, then by joining them together, we should get a speed less than eight elbows; 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 the true causes and 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.