History of Classical Mechanics

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This article covers the development of classical mechanics as part of the history of physics , from its antecedent to the present day. It was essentially founded in the 17th century by the work of Isaac Newton and was thus the first natural science in the modern sense. The presentation is based on a historical aspect and almost completely dispenses with mathematical formulas. For a more detailed explanation of the individual terms and methods, please refer to the relevant articles.

Antiquity to Galileo

Until the beginning of the 17th century, mechanics were limited to statics . Archimedes and his two founders in the 3rd century BC u. Z. formulated laws of equilibrium at the lever and of Archimedes principle for hydrostatic buoyancy . It was not until the 16th century AD. At present, these laws were extended by Simon Stevin to the equilibrium of more than two forces by specifying the closed force corner as the equilibrium condition. Stevin was also the first to derive the equilibrium condition for the downhill force acting on the inclined plane . Power was generally considered to be an inherent ability of the individual body to achieve a certain effect (or to prevent, e.g. falling another object). In order to have an effect in the sense of mechanics, a body had to touch another body in order to push, pull, lift, push or push it, the latter suddenly changing its speed. The correct distinction was not made between mass and weight .

From the time of Aristotle to the 16th century, movement was regarded as something absolutely contrary to calm. Therefore, z. For example, the explanation of a gradual (steady) transition from rest to movement is a philosophically insoluble problem. For the free fall of earthly bodies, it was not an external influence that was held responsible, but a natural downward tendency inherent in every heavy body. It was assumed for the heavenly bodies that they perpetually carry out the natural movement in the form of a uniform circular movement, free from the mechanical effects mentioned above.

The departure from such views, which had been widespread for centuries, marked the beginning of classical mechanics and modern science in general in the 17th century. It is mainly thanks to Galileo Galilei . He opposed the philosophical-theological speculation that had prevailed in natural philosophy up to that point with his new experimental method, which starts from observations, if possible measurements, and analyzes them with mathematical rigor. For the knowledge gained in this way, he also demanded that, in case of doubt, they should take precedence over those obtained from speculation.

At the same time, Johannes Kepler , based solely on the observed positions of the planets, formulated Kepler's laws , according to which the planets move with variable speed on elliptical orbits around the sun.

Instead of trying to deduce the form of natural movement from generally applicable philosophical principles, as before, Galileo took the observation of real, concrete sequences of movements as his starting point. He was the first to carry out specifically planned experiments in order to observe these processes directly, measure them as precisely as possible and then analyze the measured values ​​using mathematical methods. From this he gained fundamental general insights and new concepts that are still valid today through generalization and idealization. Examples include the uniformly accelerated movement , in which, according to the laws of fall, the instantaneous velocity increases proportionally to the time of fall, the trajectory parabola , which is explained by the combination (p. 42) of a horizontal non-accelerated movement with a vertical accelerated movement, and the pendulum laws , according to which at small deflections, the period of oscillation is determined by nothing other than the length of the suspension thread. Galileo also came very close to the principle of inertia , according to which an uninfluenced body does not follow a circular path but a uniform movement in a straight line, and the principle of relativity , according to which there is no fundamental difference between rest and movement. (Pp. 10, 19) These two principles, which are still valid today, were not yet clearly stated by Galileo, but shortly afterwards by René Descartes . (P. 59) and Christiaan Huygens .

The mechanics of Isaac Newton

Isaac Newton made the developmental step towards fully developed mechanics in his major work Mathematical Principles of the Philosophy of Nature , published in 1687 . In it Newton initially assigned an unchangeable mass to each body and then a quantity of motion that is the product of mass and instantaneous speed (today's name: momentum ). By blaming an externally “impressed force” without exception for when the size of a body's movement changes, he gave the force its ultimate central role in mechanics. Without looking for further explanations about the nature, the cause or the mode of operation of the force ( “ Hypotheses non fingo ” - I do not make hypotheses ; what is meant are the old philosophical speculations), he defined the change it caused as a measure of a certain impressed force the magnitude of the movement itself, both in terms of its magnitude and its direction. With these concepts and many experiments of his own, Newton succeeded in comprehensively describing the movements of the body. A constant force z. B., which acts in the direction of speed, only changes the amount of movement and leads to a movement like free fall; If the force is always perpendicular to the velocity at a constant amount, it only changes the direction of the magnitude of the movement and thus leads to a uniform circular movement. In particular, Newton was able to analyze the real movements that z. B. deviate from their ideal, previously regarded as "natural" shape due to friction. He succeeded in tracing the movement of the earth, the planets and its moons, including their already known irregularities, as well as the tides and the movements of falling and swinging bodies, to the action of a single kind of force, for which he could give a simple universal law , Newton's law of gravitation . However, Newton's mechanics were essentially limited to the movements of individual bodies or mass points, even if he was already dealing with flow, friction and sound in liquid or gaseous substances. The peculiarities of the mechanics of extended bodies, where rotational movement and deformation are also possible, remained largely beyond consideration.

Elaboration of the classical mechanics

At Newton's time, other scientists were also working intensively on problems in mechanics and contributed essential findings. Mention should be made among others Christiaan Huygens ( relativity principle , shock laws , physical pendulum ), Robert Hooke ( Hooke's law of elasticity, spring oscillations), Gottfried Wilhelm Leibniz (preparation of the concept of kinetic energy ), Johann I Bernoulli (model concept that in an accelerated solid Body each part remains in its place relative to the body because it is accelerated accordingly by suitable forces exerted on it by the adjacent parts). Together with the other developments that were achieved during the 18th and 19th centuries by Leonhard Euler , Jean-Baptiste le Rond d'Alembert , Joseph-Louis de Lagrange , Pierre-Simon Laplace , William Rowan Hamilton (and others), this whole theory was called Newtonian mechanics or rational mechanics and from 1900 it was also called classical mechanics .

Basics, point mechanics, extended bodies

An important step towards classical mechanics was the precise formulation of Newton's mechanics by Leonhard Euler (1736) in the form of the differential calculus invented by Leibniz (Newton himself only presented geometrical proofs in his writings). For the first time, what is now known as “2. Newton's Law ”known differential equation (in today's notation ), in which the rate of change of the quantity of motion is fully identified with the acting force instead of just being viewed as its measure. Furthermore, Euler differentiated correctly for the first time between the mass point in Newton's mechanics and the rigid body and gave the formulas for its dynamics. In particular, the laws of rotary motion he formulated with the terms angular velocity , torque , moment of inertia and main axes of inertia were important for the further development of Newtonian mechanics and their technical application in the early machine age.

In 1743, Jean-Baptiste le Rond d'Alembert published the method of calculating the movements of many bodies (mass points) that not only act on one another, but are also kept on certain paths by constraining forces.

With the cutting principle laid Euler in 1752 the general basis, to treat extensive (including deformable or liquid) body: if any part of a body in thought cut out , he followed the Newtonian laws of mechanics itself, the forces acting on it, the that the rest of the body exerts on it at the cut surfaces (plus any external forces such as weight etc.). [S. 92] Thus, extended bodies could also be understood as systems of many mass points and treated with the means of Newton's point mechanics .

In 1744, Pierre Louis Moreau de Maupertuis discovered the concept of effect and the principle of the smallest effect , to which all mechanical processes are subject.

On this basis, Joseph-Louis de Lagrange developed the branch of classical mechanics in 1788, which is more precisely referred to as analytical mechanics . With the help of generalized coordinates and the newly introduced Lagrangian function, the equations of motion of any mechanical systems can be set up. This method is also used today as a starting point for the equations of motion in quantum field theory .

In 1796, Pierre-Simon Laplace brought celestial mechanics to a level that made it possible to derive the existence of the planet Neptune from the unexplained rest of the orbital disturbances of the planet Uranus and to calculate its approximate coordinates.

William Rowan Hamilton published a further development of Lagrange's method in 1835, which not only uses the Hamilton function to provide the equations of motion of any mechanical systems, but also shows a deep parallel between point mechanics and geometrical optics in the Hamilton-Jacobian differential equation . Werner Heisenberg was able to build quantum mechanics on this in 1925 .

Hydromechanics

Just as important was the extension of Newtonian mechanics to the dynamics of flowing liquids and gases ( hydrodynamics , aerodynamics ). These applications are just as relevant for flows in canals and pipe systems as they are for the driving resistance of ships. First Daniel Bernoulli was successful here in 1738, then Leonhard Euler in particular. For the final breakthrough to practical applicability with real, viscous liquids, the internal friction losses were not yet taken into account. Claude Louis Marie Henri Navier (1822) and George Gabriel Stokes (1845) succeeded in doing this, and their Navier-Stokes equations are still the basic equations for calculating flows today.

Elasticity theory and mechanics of continuous media

In the area of statics , as early as 1638, Galileo tried to calculate the breaking strength of a beam as a function of length, width and height and derived a - albeit not entirely correct - formula. After Robert Hooke discovered the law of elasticity ( Hooke's law ) in 1678 , Jakob I Bernoulli , Leibniz, Euler and others improved the erroneous prefactor in Galileo's equation step by step, but the correct form was only derived by Charles Augustin de Coulomb in 1773 . Today's differential equation of beam bending, which also describes the vibrations of beams, was first given by Navier in 1821.

The consideration of dynamic elastic phenomena had already begun a few years before Newton's Principia (1687) with Robert Hooke. In 1678 he was able to deduce from his Basic Law of Elasticity that the period of oscillation of spring pendulums is independent of the deflection, which is now considered a characteristic of harmonic oscillation . Hooke's concept of force did not correspond to that of Newton at the time, but Newton found the same result in the Principia when he analyzed movements on elliptical orbits when the center of force is in their center. Newton also explained sound as an elastic oscillation in air. The analysis of the movement of a vibrating string was started in 1713 by Brook Taylor (known for the Taylor expansion in differential calculus) and continued by Leibniz, Johann I Bernoulli , d'Alembert, Euler. Daniel Bernoulli finally found in 1753 that the general form of the string oscillation can always be represented as a superposition of the fundamental oscillation of the string and its overtones - an anticipation of the Fourier decomposition by 60 years.

For a long time, the application of Newtonian mechanics to the internal movements of deformable (e.g. elastic) bodies remained a problem. The term stress tensor , which is central to today's continuum mechanics , was correctly introduced by Augustin Louis Cauchy in 1822 .

Technical mechanics

Since ancient times, the simple machines (wheel, lever, pulley, inclined plane, etc.), the water wheels, canals, dams, locks and ships, the supporting structures of houses, protective walls and mines as well as the military arsenal for attack and defense, etc. traditional rules of craftsmanship, engineering and construction and have repeatedly been made the subject of mechanics. However, “ technical mechanics ” began to develop as an independent branch of classical mechanics only in the 19th century, when the increasingly complex machines and structures (e.g. suspension bridges, steel towers) required new construction methods. For the mechanical problems that occurred due to the well-known forces such as weight, wind and water pressure in connection with steel and suspension bridges, locomotives and steamships, the statics (and structural statics ) were initially significantly further developed. In the second half of the 19th century, the dynamic approach was added, because with machines running faster and faster, the inertial forces also reached significant magnitudes, which were caused by the accelerated movement of the machine parts. From the beginning of the 20th century, technical mechanics also took into account that elastic deformations caused by an external force can be increased many times over by mechanical resonance if the force changes periodically. More than half a century earlier, a suspension bridge had been brought down for the first time by a group of marching soldiers causing it to vibrate (see Broughton Suspension Bridge ). Other important branches of technical mechanics are fluid mechanics , especially for turbulent flow (from the end of the 19th century), and the finite element method , which emerged in the field of aircraft construction in the middle of the 20th century and is now used for a large number of other constructions .

Chaos theory

In the second half of the 20th century, chaos research emerged within the framework of classical mechanics . For numerous systems of classical mechanics from the simple double pendulum to the turbulent flow, which follow the deterministic classical equations of motion, it was shown under which circumstances they behave chaotically, i.e. H. with the smallest differences in the initial conditions develop completely differently. For more information see under Deterministic Chaos .

Mechanistic worldview

The success that classical mechanics had in the course of the 18th and 19th centuries in explaining countless phenomena in nature and technology led to the widespread view that one could possibly understand the whole world in a mechanical way. All processes, from the celestial phenomena to the chemical changes and the refraction of light to the human spirit, should be traced back to the movement of material bodies under the influence of mutual forces. Outstanding representatives of this development were, among others, Pierre-Simon Laplace , Claude-Louis Berthollet and Jean-Baptiste Biot . A mechanistic worldview emerged, eventually became the paradigm of scientific rationality in general and has remained so in a modified form to this day. For more information, see also under Laplace's demon , natural theory , machine paradigm . This way of thinking, however, met with bitter opposition at many German universities, where the philosophical faculties in particular were responsible for physics as a prerequisite for studying philosophy. There they resisted the penetration of experimental philosophy , originally from England , which instead of genuine philosophical ultimate explanations on the basis of deepest principles only produces superficial descriptions of connections between observable phenomena, but gives them the wrong appearance through the extensive use of mathematical methods the science. In the romantic natural philosophy of German idealism , this criticism culminated in a fundamental rejection of modern natural science in the manner justified by Newton at the beginning of the 19th century. This rejection can still be found today in the form of mutual disdain for natural and human sciences. One of the last great philosophical exponents of this way of thinking was Georg Wilhelm Friedrich Hegel in 1830. The last physics professor to be inspired by him was Georg Friedrich Pohl in Breslau, who in 1845 tried unsuccessfully to reformulate Newtonian celestial mechanics according to the principles of romantic philosophy.

Individual evidence

  1. ^ Moritz Rühlmann: Lectures on the history of technical mechanics and theoretical machine theory and the related mathematical sciences . Baumgärtner, Leipzig 1885. Reprint: Documenta technica, series 1, presentations on the history of technology, Verlag Olms, Hildesheim 1979
  2. ^ A b c d e Richard Westfall: Force in Newton's Physics: the Science of Dynamics in the Seventeenth Century . MacDonald, London 1971.
  3. ^ Isaac Newton (translated by J. Ph. Wolfers ): Mathematische Principien der Naturlehre , Verlag R. Oppenheim, Berlin 1872 Online .
  4. ↑ Isaac Newton: The Mathematical Principles of Physics ; translated and edited by Volkmar Schüller. - de Gruyter, Berlin (ua) 1999. ISBN 3-11-016105-2 (following the third edition, with additional material such as reviews of the three editions during Newton's lifetime and texts deleted by Newton from the first edition)
  5. ^ Clifford Truesdell: A program toward rediscovering the rational mechanics of the age of reason. In: Archive for history of exact sciences . tape 1 , no. 1 , 1960, p. 1-36 .
  6. ↑ a b István Szabó : History of mechanical principles and their most important applications . 3. Edition. Birkhäuser, Basel 1987.
  7. ^ Clifford Truesdell: A program toward rediscovering the rational mechanics of the age of reason. In: Archive for history of exact sciences . tape 1 , no. 1 , 1960, p. 1-36 .
  8. ↑ Felix Klein: About technical mechanics , in: Friedrich Schilling et al .: About applied mathematics and physics: in their importance for teaching in higher schools . BG Teubner, 1900.
  9. ^ F. Auerbach: Mechanik , in A. Winkelmann (Ed.): Handbuch der Physik Vol. 1.1, Verlag Joh. Amb. Barth, Leipzig 1908, pp. 211ff
  10. ^ Leonhard Euler: Mechanica sive motus scientia analytice exposita . 2 volumes, 1736 ( E015 , E016 )
  11. ^ Leonhard Euler: Découverte d'un nouveau principe de Mécanique . In: Mémoires de l'académie des sciences de Berlin . Volume 6, 1752, pp. 185-217 ( E177 ).
  12. ^ Jean-Baptiste le Rond d'Alembert: Traité de dynamique. (1743 or 1758)
  13. ^ Jean-Baptiste le Rond d'Alembert: Traité de l'équilibre et du mouvement des fluides: pour servir de suite au Traité de dynamique. (1744)
  14. ^ Otto Bruns, Theodor Lehmann: Elements of Mechanics I: Introduction, Statics . Vieweg, Braunschweig 1993. [1]
  15. ^ Pierre Louis Moreau de Maupertuis: Principe de la moindre quantité d'action pour la mécanique (1744); ders .: Essai de cosmologie , Amsterdam 1750, German attempt at a cosmology: translated from the French . Nicolai, 1751, p. 89.
  16. ^ Joseph-Louis de Lagrange: Mécanique Analytique , Paris: Desaint 1788, 2nd edition in 2 volumes, Paris: Courcier, 1811–1815; German translation by Friedrich Murhard: Analytische Mechanik , Göttingen, Vandenhoeck and Ruprecht 1797, the translation of the 4th edition by H. Servus was published by J. Springer in 1887
  17. ↑ Pierre-Simon Laplace: Traité de mécanique céleste , five volumes, Paris 1798–1825 (reprint, Brussels 1967)
  18. ^ Pierre-Simon Laplace: Exposition du système du monde , Paris 1796; translated by Johann Karl Friedrich Hauff: Representation of the world system , Frankfurt 1797
  19. ^ William Rowan Hamilton: Second Essay On a General Method in Dynamics. In: Philosophical Transactions of the Royal Society of London 125 (1835), pp. 95-144. Philosophical Transactions of the Royal Society of London . W. Bowyer and J. Nichols for Lockyer Davis, printer to the Royal Society, 1835, p. 95.
  20. ^ Karl-Eugen Kurrer : The History of the Theory of Structures. Searching for Equilibrium . Ernst & Sohn , Berlin 2018, ISBN 978-3-433-03229-9
  21. ↑ Gunter Lind: Physics in textbooks 1700-1850 . Springer, Berlin 1992, ISBN 3-540-55138-7 .
  22. ^ Rudolf Stichweh: On the emergence of the modern system of scientific disciplines: Physics in Germany 1740-1890 . Suhrkamp, ​​1984.
  23. ↑ Erhard Scheibe: The Philosophy of Physicists . 2nd Edition. CH Beck, Munich 2012, p. 22nd ff .
  24. ^ CP Snow: The Two Cultures. 1959. In: Helmut Kreuzer (Ed.): The two cultures. Literary and scientific intelligence. CP Snow's thesis under discussion. dtv, Munich 1987, ISBN 3-423-04454-3
  25. ↑ Georg Wilhelm Friedrich Hegel: Encyclopedia of the Philosophical Sciences in Outlines, Part Two. The natural philosophy . 3. Edition. 1830. Hegel complains there (§270, see also §137): “ ... the inundation of physical mechanics with unspeakable metaphysics which - contrary to experience and concept - has those mathematical determinations as its source alone. "
  26. ↑ Georg Friedr. Pohl: Foundation of the three Keppler's laws, especially by tracing the third law back to a newly discovered far more general basic law of cosmic movements, which takes the place of Newton's law of gravitation. Georg Philipp Aderholz, Breslau 1845.