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The following is a timeline of the
history of classical mechanics In physics, mechanics is the study of objects, their interaction, and motion; classical mechanics is mechanics limited to non-relativistic and non-quantum approximations. Most of the techniques of classical mechanics were developed before 1900 so ...
:


Antiquity

* 4th century BC –
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
invents the system of
Aristotelian physics Aristotelian physics is the form of natural philosophy described in the works of the Greek philosopher Aristotle (384–322 BC). In his work ''Physics'', Aristotle intended to establish general principles of change that govern all natural bodies ...
, which is later largely disproved * 4th century BC – Babylonian astronomers calculate Jupiter's position using the
Trapezoidal rule In calculus, the trapezoidal rule (or trapezium rule in British English) is a technique for numerical integration, i.e., approximating the definite integral: \int_a^b f(x) \, dx. The trapezoidal rule works by approximating the region under the ...
* 260 BC –
Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
works out the principle of the
lever A lever is a simple machine consisting of a beam (structure), beam or rigid rod pivoted at a fixed hinge, or '':wikt:fulcrum, fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, l ...
and connects buoyancy to weight * 60 –
Hero of Alexandria Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimental ...
writes ''Metrica, Mechanics'' (on means to lift heavy objects), and ''Pneumatics'' (on machines working on pressure) * 350 –
Themistius Themistius ( ; 317 – c. 388 AD), nicknamed Euphrades (, "''eloquent''"), was a statesman, rhetorician and philosopher. He flourished in the reigns of Constantius II, Julian, Jovian, Valens, Gratian and Theodosius I, and he enjoyed the favo ...
states, that
static friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...
is larger than
kinetic friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...


Early mechanics

* 6th century –
John Philoponus John Philoponus ( Greek: ; , ''Ioánnis o Philóponos''; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Coptic Miaphysite philologist, Aristotelian commentator and Christian theologian from Alexandria, Byza ...
introduces the concept of impetus and the theory was modified by
Avicenna Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian ...
in the 11th century and Ibn Malka al-Baghdadi in the 12th century * 6th century –
John Philoponus John Philoponus ( Greek: ; , ''Ioánnis o Philóponos''; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Coptic Miaphysite philologist, Aristotelian commentator and Christian theologian from Alexandria, Byza ...
says that by observation, two balls of very different weights will fall at nearly the same speed. He therefore tests the
equivalence principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
* 1021 –
Al-Biruni Abu Rayhan Muhammad ibn Ahmad al-Biruni (; ; 973after 1050), known as al-Biruni, was a Khwarazmian Iranian scholar and polymath during the Islamic Golden Age. He has been called variously "Father of Comparative Religion", "Father of modern ...
uses three
orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ...
coordinates to describe point in space: * 1100–1138 –
Avempace Abū Bakr Muḥammad ibn Yaḥyà ibn aṣ-Ṣā’igh at-Tūjībī ibn Bājja (), known simply as Ibn Bajja () or his Latinized name Avempace (;  – 1138), was an Arab polymath, whose writings include works regarding astronomy, physic ...
develops the concept of a fatigue, which according to Shlomo Pines is precursor to Leibnizian idea of force * 1100–1165 – Hibat Allah Abu'l-Barakat al-Baghdaadi discovers that
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
is proportional to acceleration rather than speed, a fundamental law in classical mechanics * 1340–1358 –
Jean Buridan Jean Buridan (; ; Latin: ''Johannes Buridanus''; – ) was an influential 14thcentury French scholastic philosopher. Buridan taught in the faculty of arts at the University of Paris for his entire career and focused in particular on logic and ...
develops the
theory of impetus The theory of impetus, developed in the Middle Ages, attempts to explain the forced motion of a body, what it is, and how it comes about or ceases. It is important to note that in ancient and medieval times, motion was always considered absolute, ...
* 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. 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 * 1500–1528 – Al-Birjandi develops the theory of "circular
inertia Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...
" to explain
Earth's rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in progra ...
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 Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...
.
* 16th century – Francesco Beato and
Luca Ghini Luca Ghini ( Casalfiumanese, 1490 – Bologna, 4 May 1556) was an Italian physician and botanist, notable as the creator of the first recorded herbarium, as well as the first botanical garden in Europe. Biography Ghini was born in Casalfiumanese ...
experimentally contradict Aristotelian view on free fall. * 16th century – Domingo de Soto suggests that bodies falling through a homogeneous medium are uniformly accelerated. 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 Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
notices the timekeeping property of the
pendulum A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate i ...
* 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 Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials sci ...
and
kinematics In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...
) where he develops, amongst other things,
Galilean transformation In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotati ...
* 1644 –
René Descartes René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramou ...
suggests an early form of the law of
conservation of momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...
* 1645 – Ismaël Bullialdus argues that "gravity" weakens as the inverse square of the distance * 1651 –
Giovanni Battista Riccioli Giovanni Battista Riccioli (17 April 1598 – 25 June 1671) was an Italian astronomer and a Catholic priest in the Jesuit order. He is known, among other things, for his experiments with pendulums and with falling bodies, for his discussion of ...
and
Francesco Maria Grimaldi Francesco Maria Grimaldi (2 April 1618 – 28 December 1663) was an Italian Jesuit priest, mathematician and physicist who taught at the Jesuit college in Bologna. He was born in Bologna to Paride Grimaldi and Anna Cattani. Work Between 164 ...
discover the
Coriolis effect In physics, the Coriolis force is a pseudo force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the moti ...
* 1658 –
Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...
experimentally discovers that balls placed anywhere inside an inverted
cycloid In geometry, a cycloid is the curve traced by a point on a circle as it Rolling, rolls along a Line (geometry), straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette (curve), roulette, a curve g ...
reach the lowest point of the cycloid in the same time and thereby experimentally shows that the cycloid is the
tautochrone A tautochrone curve or isochrone curve () is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time ...
* 1668 –
John Wallis John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...
suggests the law of conservation of momentum * 1673 –
Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...
publishes his ''
Horologium Oscillatorium (English language, English: ''The Pendulum Clock: or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks'') is a book published by Dutch mathematician and physicist Christiaan Huygens in 1673 and his major work on p ...
''. Huygens describes in this work the first two laws of motion. The book is also the first modern treatise in which a physical problem (the accelerated motion of a falling body) is idealized by a set of parameters and then analyzed mathematically. * 1676–1689 –
Gottfried Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...
develops the concept of
vis viva ''Vis viva'' (from the Latin for "living force") is a historical term used to describe a quantity similar to kinetic energy in an early formulation of the principle of conservation of energy. Overview Proposed by Gottfried Leibniz over the period ...
, a limited theory of
conservation of energy The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...
* 1677 –
Baruch Spinoza Baruch (de) Spinoza (24 November 163221 February 1677), also known under his Latinized pen name Benedictus de Spinoza, was a philosopher of Portuguese-Jewish origin, who was born in the Dutch Republic. A forerunner of the Age of Enlightenmen ...
puts forward a primitive notion of Newton's first law


Newtonian mechanics

* 1687 –
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
publishes his ''
Philosophiæ Naturalis Principia Mathematica (English: ''The Mathematical Principles of Natural Philosophy''), often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Lati ...
'', in which he formulates
Newton's laws of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
and
Newton's law of universal gravitation Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is Proportionality (mathematics)#Direct proportionality, proportional to the product ...
* 1690 – James Bernoulli shows that the
cycloid In geometry, a cycloid is the curve traced by a point on a circle as it Rolling, rolls along a Line (geometry), straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette (curve), roulette, a curve g ...
is the solution to the tautochrone problem * 1691 –
Johann Bernoulli Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...
shows that a chain freely suspended from two points will form a
catenary In physics and geometry, a catenary ( , ) is the curve that an idealized hanging chain or wire rope, cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, ...
* 1691 – James Bernoulli shows that the catenary curve has the lowest
center of gravity In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For ...
of any chain hung from two fixed points * 1696 – Johann Bernoulli shows that the cycloid is the solution to the brachistochrone problem * 1710 –
Jakob Hermann Jakob Hermann (16 July 1678 – 11 July 1733) was a mathematician who worked on problems in classical mechanics. He is the author of ''Phoronomia'', an early treatise on mechanics in Latin, which has been translated by Ian Bruce in 2015-16. In 172 ...
shows that
Laplace–Runge–Lenz vector In classical mechanics, the Laplace–Runge–Lenz vector (LRL vector) is a vector (geometric), vector used chiefly to describe the shape and orientation of the orbit (celestial mechanics), orbit of one astronomical body around another, such as a ...
is conserved for a case of the inverse-square
central force In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force. \mathbf(\mathbf) = F( \mathbf ) where F is a force vector, ''F'' is a scalar valued force function (whose abso ...
* 1714 – Brook Taylor derives the
fundamental frequency The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a n ...
of a stretched vibrating string in terms of its tension and mass per unit length by solving an ordinary differential equation * 1733 –
Daniel Bernoulli Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applicati ...
derives the fundamental frequency and
harmonic In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
s 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 Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
solves the ordinary differential equation for a forced harmonic oscillator and notices the
resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
* 1742 –
Colin Maclaurin Colin Maclaurin (; ; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. He is also known for being a child prodigy and holding the record for being the youngest professor. ...
discovers his uniformly rotating self-gravitating spheroids * 1743 –
Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert ( ; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopé ...
publishes his ''Traite de Dynamique'', in which he introduces the concept of
generalized forces In analytical mechanics (particularly Lagrangian mechanics), generalized forces are conjugate to generalized coordinates. They are obtained from the applied forces , acting on a system that has its configuration defined in terms of generalized ...
and
D'Alembert's principle D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical physics, classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d' ...
* 1747 – D'Alembert and
Alexis Clairaut Alexis Claude Clairaut (; ; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Isaac Newton, Sir Isaa ...
publish first approximate solutions to the
three-body problem In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other in space and then calculate their subsequent trajectories using Newton' ...
* 1749 –
Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
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 Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...
solutions * 1776 –
John Smeaton John Smeaton (8 June 1724 – 28 October 1792) was an English civil engineer responsible for the design of bridges, canals, harbours and lighthouses. He was also a capable mechanical engineer and an eminent scholar, who introduced various ...
publishes a paper on experiments relating power,
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...
,
momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...
and
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
, and supporting the conservation of energy


Analytical mechanics

* 1788 –
Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaLagrange's equations of motion in the ''Méchanique Analytique'' * 1798 –
Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...
publishes his
Traité de mécanique céleste ''Traité de mécanique céleste'' () is a five-volume treatise on celestial mechanics written by Pierre-Simon Laplace and published from 1798 to 1825 with a second edition in 1829. In 1842, the government of Louis Philippe gave a grant of 40,000 ...
vol.1 and lasts vol.5 in 1825. In this, he summarized and extended the work of his predecessors * 1803 – Louis Poinsot develops idea of angular momentum conservation (this result was previously known only in the case of conservation of
areal velocity In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is a pseudovector whose vector length, length equals the Rate of change (mathematics), rate of change at which area is swept out by a particle as it moves ...
) * 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 In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mecha ...
* 1829 –
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...
introduces Gauss's principle of least constraint * 1834 – Carl Jacobi discovers his uniformly rotating self-gravitating ellipsoids * 1834 – Louis Poinsot notes an instance of the intermediate axis theorem * 1835 – William Hamilton states Hamilton's canonical equations of motion * 1838 – Liouville begins work on Liouville's theorem * 1841 – Julius von Mayer, an
amateur An amateur () is generally considered a person who pursues an avocation independent from their source of income. Amateurs and their pursuits are also described as popular, informal, autodidacticism, self-taught, user-generated, do it yourself, DI ...
scientist, writes a paper on the conservation of energy but his lack of academic training leads to a priority dispute. * 1847 –
Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (; ; 31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The ...
formally states the law of
conservation of energy The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...
* first half of the 19th century –
Cauchy Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real a ...
develops his momentum equation and his stress tensor * 1851 –
Léon Foucault Jean Bernard Léon Foucault (, ; ; 18 September 1819 – 11 February 1868) was a French physicist best known for his demonstration of the Foucault pendulum, a device demonstrating the effect of Earth's rotation. He also made an early measuremen ...
shows the Earth's rotation with a huge
pendulum A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate i ...
(
Foucault pendulum The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault, conceived as an experiment to demonstrate the Earth's rotation. If a long and heavy pendulum suspended from the high roof above a circu ...
) * 1870 –
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
deduces
virial theorem In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path), with ...
* 1890 –
Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...
discovers the sensibility of initial conditions in the
three-body problem In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other in space and then calculate their subsequent trajectories using Newton' ...
. * 1898 –
Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations. Biography The son of a tea ...
discusses the Hadamard billiards.


Modern developments

* 1900 –
Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
introduces the idea of quanta, introducing
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
* 1902 –
James Jeans Sir James Hopwood Jeans (11 September 1877 – 16 September 1946) was an English physicist, mathematician and an astronomer. He served as a secretary of the Royal Society from 1919 to 1929, and was the president of the Royal Astronomical Soci ...
finds the length scale required for gravitational perturbations to grow in a static nearly homogeneous medium * 1905 –
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
first mathematically describes
Brownian motion Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical ...
and introduces
relativistic mechanics In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non- quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities o ...
* 1915 –
Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
proves
Noether's theorem Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This is the first of two theorems (see Noether's second theorem) published by the mat ...
, from which conservation laws are deduced * 1915 –
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
introduces
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
* 1923 –
Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...
introduces the geometrized Newtonian gravitation, treating Newtonian gravitation in terms of spacetime. * 1931–1932 –
Bernard Koopman Bernard Osgood Koopman (January 19, 1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research. Education and work ...
and
John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
papers led to the development of Koopman–von Neumann classical mechanics. * 1952 – Parker develops a
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...
form of the virial theorem * 1954 –
Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...
publishes the first version of the Kolmogorov–Arnold–Moser theorem. * 1961 – Edward Norton Lorenz discovers Lorenz systems and establishes the field of
chaos theory Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...
. * 1978 –
Vladimir Arnold Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to s ...
states precise form of Liouville–Arnold theoremV. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics (Springer, New York, 1978), Vol. 60. * 1983 – Mordehai Milgrom proposes modified Newtonian dynamics as an alternative to the
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
hypothesis * 1992 – Udwadia and Kalaba create Udwadia–Kalaba equation * 2003 – John D. Norton introduces Norton's dome


References

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