# Timeline of classical mechanics

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**Timeline of classical mechanics**:

## Early mechanics[edit]

- 4th century BC - Aristotle invents the system of Aristotelian physics, which is later largely disproved
- 4th century BC - Babylonian astronomers calculate Jupiter's position using the mean speed theorem
^{[1]} - 260 BC - Archimedes works out the principle of the lever and connects buoyancy to weight
- 60 - Hero of Alexandria writes
*Metrica, Mechanics*(on means to lift heavy objects), and*Pneumatics*(on machines working on pressure) - 350 - Themistius states, that static friction is larger than kinetic friction
^{[2]} - 6th century - John Philoponus says that by observation, two balls of very different weights will fall at nearly the same speed. He therefore tests the equivalence principle
- 1021 - Al-Biruni uses three orthogonal coordinates to describe point in space
^{[3]} - 1000-1030 - Alhazen and Avicenna develop the concepts of inertia and momentum
- 1100-1138 - Avempace develops the concept of a reaction force
^{[4]} - 1100-1165 - Hibat Allah Abu'l-Barakat al-Baghdaadi discovers that force is proportional to acceleration rather than speed, a fundamental law in classical mechanics
^{[5]} - 1121 - Al-Khazini publishes
*The Book of the Balance of Wisdom*, in which he develops the concepts of gravity at-a-distance. He suggests that the gravity varies depending on its distance from the center of the universe, namely Earth^{[6]} - 1340-1358 - Jean Buridan develops the theory of impetus
- 14th century - Oxford Calculators and French collaborators prove the mean speed theorem
- 14th century - Nicole Oresme derives the times-squared law for uniformly accelerated change.
^{[7]}Oresme, however, regarded this discovery as a purely intellectual exercise having no relevance to the description of any natural phenomena, and consequently failed to recognise any connection with the motion of accelerating bodies^{[8]} - 1500-1528 - Al-Birjandi develops the theory of "circular inertia" to explain Earth's rotation
^{[9]} - 16th century - Francesco Beato and Luca Ghini experimentally contradict aristotelian view on free fall
^{[10]}. - 16th century - Domingo de Soto suggests that bodies falling through a homogeneous medium are uniformly accelerated.
^{[11]}^{[12]}Soto, however, did not anticipate many of the qualifications and refinements contained in Galileo's theory of falling bodies, he did not, for instance, recognise, as Galileo did, that a body would fall with a strictly uniform acceleration only in a vacuum, and that it would otherwise eventually reach a uniform terminal velocity - 1581 - Galileo Galilei notices the timekeeping property of the pendulum
- 1589 - Galileo Galilei uses balls rolling on inclined planes to show that different weights fall with the same acceleration
- 1638 - Galileo Galilei publishes
*Dialogues Concerning Two New Sciences*(which were materials science and kinematics) where he develops, amongst other things, Galilean transformation - 1645 - Ismaël Bullialdus argues that "gravity" weakens as the inverse square of the distance
^{[13]} - 1651 - Giovanni Battista Riccioli and Francesco Maria Grimaldi discover the Coriolis effect
- 1658 - Christiaan Huygens experimentally discovers that balls placed anywhere inside an inverted cycloid reach the lowest point of the cycloid in the same time and thereby experimentally shows that the cycloid is the tautochrone
- 1668 - John Wallis suggests the law of conservation of momentum
- 1676-1689 - Gottfried Leibniz develops the concept of vis viva, a limited theory of conservation of energy

## Formation of classical mechanics (sometimes referred to as Newtonian mechanics)[edit]

- 1687 - Isaac Newton publishes his
*Philosophiae Naturalis Principia Mathematica*, in which he formulates Newton's laws of motion and Newton's law of universal gravitation - 1690 - James Bernoulli shows that the cycloid is the solution to the tautochrone problem
- 1691 - Johann Bernoulli shows that a chain freely suspended from two points will form a catenary
- 1691 - James Bernoulli shows that the catenary curve has the lowest center of gravity of any chain hung from two fixed points
- 1696 - Johann Bernoulli shows that the cycloid is the solution to the brachistochrone problem
- 1707 - Gottfried Leibniz probably develops the principle of least action
- 1710 - Jakob Hermann shows that Laplace–Runge–Lenz vector is conserved for a case of the inverse-square central force
^{[14]} - 1714 - Brook Taylor derives the fundamental frequency of a stretched vibrating string in terms of its tension and mass per unit length by solving an ordinary differential equation
- 1733 - Daniel Bernoulli derives the fundamental frequency and harmonics of a hanging chain by solving an ordinary differential equation
- 1734 - Daniel Bernoulli solves the ordinary differential equation for the vibrations of an elastic bar clamped at one end
- 1739 - Leonhard Euler solves the ordinary differential equation for a forced harmonic oscillator and notices the resonance phenomenon
- 1742 - Colin Maclaurin discovers his uniformly rotating self-gravitating spheroids
- 1743 - Jean le Rond d'Alembert publishes his "Traite de Dynamique", in which he introduces the concept of generalized forces and D'Alembert's principle
- 1747 - d'Alembert and Alexis Clairaut publish first approximate solutions to the three-body problem
- 1749 - Leonhard Euler derives equation for Coriolis acceleration
- 1759 - Leonhard Euler solves the partial differential equation for the vibration of a rectangular drum
- 1764 - Leonhard Euler examines the partial differential equation for the vibration of a circular drum and finds one of the Bessel function solutions
- 1776 - John Smeaton publishes a paper on experiments relating power, work, momentum and kinetic energy, and supporting the conservation of energy
- 1788 - Joseph Louis Lagrange presents Lagrange's equations of motion in the
*Méchanique Analitique* - 1789 - Antoine Lavoisier states the law of conservation of mass
- 1803 - Louis Poinsot develops idea of angular momentum conservation (this result was previously known only in the case of conservation of areal velocity)
- 1813 - Peter Ewart supports the idea of the conservation of energy in his paper
*On the measure of moving force* - 1821 - William Hamilton begins his analysis of Hamilton's characteristic function and Hamilton–Jacobi equation
- 1829 - Carl Friedrich Gauss introduces Gauss's principle of least constraint
- 1834 - Carl Jacobi discovers his uniformly rotating self-gravitating ellipsoids
- 1834 - John Russell observes a nondecaying solitary water wave (soliton) in the Union Canal near Edinburgh and uses a water tank to study the dependence of solitary water wave velocities on wave amplitude and water depth
- 1835 - William Hamilton states Hamilton's canonical equations of motion
- 1838 - Liouville begins work on Liouville's theorem
- 1841 - Julius Robert von Mayer, an amateur scientist, writes a paper on the conservation of energy but his lack of academic training leads to its rejection
- 1847 - Hermann von Helmholtz formally states the law of conservation of energy
- first half of XIX century - Cauchy develops his momentum equation and his stress tensor
- 1851 - Léon Foucault shows the Earth's rotation with a huge pendulum (Foucault pendulum)
- 1870 - Rudolf Clausius deduces virial theorem
- 1902 - James Jeans finds the length scale required for gravitational perturbations to grow in a static nearly homogeneous medium
- 1915 - Emmy Noether proves Noether's theorem, from which conservation laws are deduced
- 1952 - Parker develops a tensor form of the virial theorem
^{[15]} - 1978 - Vladimir Arnold states precise form of Liouville–Arnold theorem
^{[16]} - 1983 - Mordehai Milgrom proposes Modified Newtonian dynamics
- 1992 - Udwadia and Kalaba create Udwadia–Kalaba equation

## References[edit]

**^**Ossendrijver, Mathieu (29 Jan 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph".*Science*.**351**(6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. PMID 26823423. Retrieved 29 January 2016.**^**Sambursky, Samuel (2014).*The Physical World of Late Antiquity*. Princeton University Press. pp. 65–66. ISBN 9781400858989.**^**O'Connor, John J.; Robertson, Edmund F., "Al-Biruni",*MacTutor History of Mathematics archive*, University of St Andrews.:One of the most important of al-Biruni's many texts is

*Shadows*which he is thought to have written around 1021. [...]*Shadows*is an extremely important source for our knowledge of the history of mathematics, astronomy, and physics. It also contains important ideas such as the idea that acceleration is connected with non-uniform motion, using three rectangular coordinates to define a point in 3-space, and ideas that some see as anticipating the introduction of polar coordinates.**^**Shlomo Pines (1964), "La dynamique d’Ibn Bajja", in*Mélanges Alexandre Koyré*, I, 442-468 [462, 468], Paris.

(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory",*Journal of the History of Ideas***64**(4), p. 521-546 [543]: "*Pines has also seen Avempace's idea of fatigue as a precursor to the Leibnizian idea of force which, according to him, underlies Newton's third law of motion and the concept of the "reaction" of forces.*")**^**Pines, Shlomo (1970). "Abu'l-Barakāt al-Baghdādī , Hibat Allah".*Dictionary of Scientific Biography*.**1**. New York: Charles Scribner's Sons. pp. 26–28. ISBN 0-684-10114-9.:

(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory",*Journal of the History of Ideas***64**(4), p. 521-546 [528]:*Hibat Allah Abu'l-Barakat al-Bagdadi (c.1080- after 1164/65) extrapolated the theory for the case of falling bodies in an original way in his Kitab al-Mu'tabar (The Book of that Which is Established through Personal Reflection). [...] This idea is, according to Pines, "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion]," and is thus an "anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration]."*)**^**Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", in Roshdi Rashed, ed.,*Encyclopedia of the History of Arabic Science*, Vol. 2, p. 614-642 [621], Routledge, London and New York**^**Clagett (1968, p. 561), Nicole Oresme and the Medieval Geometry of Qualities and Motions; a treatise on the uniformity and difformity of intensities known as Tractatus de configurationibus qualitatum et motuum. Madison, WI: University of Wisconsin Press. ISBN 0-299-04880-2.**^**Grant, 1996, p.103).**^**F. Jamil Ragep (2001), "Tusi and Copernicus: The Earth's Motion in Context",*Science in Context***14**(1-2), p. 145–163. Cambridge University Press.**^**"Timeline of Classical Mechanics and Free Fall".*www.scientus.org*. Retrieved 2019-01-26.**^**Sharratt, Michael (1994). Galileo: Decisive Innovator. Cambridge: Cambridge University Press. ISBN 0-521-56671-1, p. 198**^**Wallace, William A. (2004). Domingo de Soto and the Early Galileo. Aldershot: Ashgate Publishing. ISBN 0-86078-964-0 (pp.II 384, II 400, III 272)**^**Ismail Bullialdus,*Astronomia Philolaica*… (Paris, France: Piget, 1645), page 23.**^**Hermann, J (1710). "Unknown title".*Giornale de Letterati D'Italia*.**2**: 447–467.

Hermann, J (1710). "Extrait d'une lettre de M. Herman à M. Bernoulli datée de Padoüe le 12. Juillet 1710".*Histoire de l'academie royale des sciences (Paris)*.**1732**: 519–521.**^**Parker, E.N. (1954). "Tensor Virial Equations" (PDF).*Physical Review*.**96**(6): 1686–1689. Bibcode:1954PhRv...96.1686P. doi:10.1103/PhysRev.96.1686. Retrieved March 24, 2012.**^**V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics (Springer, New York, 1978), Vol. 60.