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==Newtonian mechanics== * 1687 – [[Isaac Newton]] publishes his ''[[Philosophiæ 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]]<ref>{{cite journal| last = Hermann | first = J | author-link = Jakob Hermann | date = 1710 | title = Unknown title | journal = Giornale de Letterati d'Italia | volume = 2 | pages = 447–467}}<br />{{cite journal| last = Hermann | first = J | author-link = Jakob Hermann | date = 1710 | title = Extrait d'une lettre de M. Herman à M. Bernoulli datée de Padoüe le 12. Juillet 1710 | journal = Histoire de l'Académie Royale des Sciences | volume = 1732 | pages = 519–521}}</ref> * 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 [[harmonic]]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]] solves the ordinary differential equation for a [[Harmonic oscillator#Driven harmonic oscillators|forced harmonic oscillator]] and notices the [[resonance]] * 1742 – [[Colin Maclaurin]] discovers his [[Maclaurin spheroid|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 (physics)|power]], [[Mechanical work|work]], [[momentum]] and [[kinetic energy]], and supporting the conservation of energy
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