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The following is a **timeline of classical mechanics **:

- 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 introduces the concept of impetus
^{ [3] } - 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
^{ [4] } - 1100-1138 - Avempace develops the concept of a fatigue, which according to Shlomo Pines is precursor to Leibnizian idea of force
^{ [5] } - 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
^{ [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 - 1644 - René Descartes suggests an early form of the law of conservation of momentum
- 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
- 1673 - Christiaan Huygens publishes his
*Horologium Oscillatorium*. Huygens describes in this work the first two laws of motion.^{ [14] }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 develops the concept of vis viva, a limited theory of conservation of energy
- 1677 - Baruch Spinoza puts forward a primitive notion of Newton's first law

- 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
- 1710 - Jakob Hermann shows that Laplace–Runge–Lenz vector is conserved for a case of the inverse-square central force
^{ [15] } - 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
- 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 Analytique* - 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 - Louis Poinsot notes an instance of the intermediate axis theorem
^{ [16] } - 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 a priority dispute.
- 1847 - Hermann von Helmholtz formally states the law of conservation of energy
- first half of the 19th 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
- 1890 - Henri Poincaré discovers the sensibility of initial conditions in the three-body problem.
^{ [17] } - 1898 - Jacques Hadamard discusses the Hadamard billiards.
^{ [18] }

- 1900 - Max Planck introduces the idea of quanta, introducing quantum mechanics
- 1902 - James Jeans finds the length scale required for gravitational perturbations to grow in a static nearly homogeneous medium
- 1905 - Albert Einstein first mathematically describes Brownian motion and introduces relativistic mechanics
- 1915 - Emmy Noether proves Noether's theorem, from which conservation laws are deduced
- 1915 - Albert Einstein introduces general relativity
- 1952 - Parker develops a tensor form of the virial theorem
^{ [19] } - 1954 - Andrey Kolmogorov publishes the first version of the Kolmogorov–Arnold–Moser theorem.
^{ [18] } - 1961 - Edward Norton Lorenz discovers Lorenz systems and establishes the field of chaos theory.
^{ [18] } - 1978 - Vladimir Arnold states precise form of Liouville–Arnold theorem
^{ [20] } - 1983 - Mordehai Milgrom proposes modified Newtonian dynamics as an alternative to the dark matter hypothesis
- 1992 - Udwadia and Kalaba create Udwadia–Kalaba equation
- 2003 - John D. Norton introduces Norton's dome

In physics, physical chemistry and engineering, **fluid dynamics** is a subdiscipline of fluid mechanics that describes the **flow** of fluids—liquids and gases. It has several subdisciplines, including *aerodynamics* and **hydrodynamics**. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Physics is a branch of science whose primary objects of study are matter and energy. Discoveries of physics find applications throughout the natural sciences and in technology. Historically, physics emerged from the scientific revolution of the 17th century, grew rapidly in the 19th century, then was transformed by a series of discoveries in the 20th century. Physics today may be divided loosely into classical physics and modern physics.

**Inertia** is the tendency of objects in motion to stay in motion, and objects at rest to stay at rest, unless a force causes its speed or direction to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his first law of motion. It is one of the primary manifestations of mass, one of the core quantitative properties of physical systems. Newton writes:

LAW I. Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon.

**Mechanics** is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects result in displacements or changes of an object's position relative to its environment.

**Newton's laws of motion** are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:

- A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
- When a body is acted upon by a net force, the body's acceleration multiplied by its mass is equal to the net force.
- If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

In physics, **equations of motion** are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.

In Newtonian physics, **free fall** is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.

In physics and mathematics, a **brachistochrone curve**, or curve of fastest descent, is the one lying on the plane between a point *A* and a lower point *B*, where *B* is not directly below *A*, on which a bead slides frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696.

**Solid mechanics** is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

In mathematics, a **differential equation** is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

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 the term **classical mechanics** refers to that historical era as well as the approximations. Other fields of physics that were developed in the same era, that use the same approximations, and are also considered "classical" include thermodynamics and electromagnetism.

In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times. The first extant sources discussing such theories are found in ancient Greek philosophy. This work was furthered through the Middle Ages by Indian, Islamic, and European scientists, before gaining great strides during the Renaissance and Scientific Revolution—culminating in the formulation of Newton's law of gravity. This was superseded by Albert Einstein's theory of relativity in the early 20th century.

The **theory of impetus** is an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. It was introduced by John Philoponus in the 6th century, and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century. The theory was modified by Avicenna in the 11th century and Abu'l-Barakāt al-Baghdādī in the 12th century, before it was later established in Western scientific thought by Jean Buridan in the 14th century. It is the intellectual precursor to the concepts of inertia, momentum and acceleration in classical mechanics.

A timeline of **calculus** and **mathematical analysis**.

In classical mechanics, **Euler's laws of motion** are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws.

The **balance of angular momentum** or **Euler's second law** in classical mechanics is a law of physics, stating that to alter the angular momentum of a body a torque must be applied to it.

- ↑ 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. S2CID 206644971 . Retrieved 29 January 2016. - ↑ Sambursky, Samuel (2014).
*The Physical World of Late Antiquity*. Princeton University Press. pp. 65–66. ISBN 9781400858989. - ↑ Sorabji, Richard (2010). "John Philoponus".
*Philoponus and the Rejection of Aristotelian Science*(2nd ed.). Institute of Classical Studies, University of London. p. 47. ISBN 978-1-905-67018-5. JSTOR 44216227. OCLC 878730683. - ↑ 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*. Vol. 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]."*) - ↑ 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. - ↑ Rob Iliffe & George E. Smith (2016).
*The Cambridge Companion to Newton*. Cambridge University Press. p. 75. ISBN 9781107015463. - ↑ 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'Académie Royale des Sciences*.**1732**: 519–521. - ↑ Poinsot (1834)
*Theorie Nouvelle de la Rotation des Corps*, Bachelier, Paris - ↑ Poincaré, H. (January 1900). "Introduction".
*Acta Mathematica*.**13**(1–2): 5–7. doi: 10.1007/BF02392506 . ISSN 0001-5962. - 1 2 3 Oestreicher, Christian (2007-09-30). "A history of chaos theory".
*Dialogues in Clinical Neuroscience*.**9**(3): 279–289. doi:10.31887/DCNS.2007.9.3/coestreicher. ISSN 1958-5969. PMC 3202497 . PMID 17969865. - ↑ Parker, E.N. (1954). "Tensor Virial Equations".
*Physical Review*.**96**(6): 1686–1689. Bibcode:1954PhRv...96.1686P. doi:10.1103/PhysRev.96.1686. - ↑ V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics (Springer, New York, 1978), Vol. 60.

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