- History of classical mechanics
**Early Ideas on Motion**The Greek philosophers, and

Aristotle in particular, were the first to propose that there are abstract principles governing nature. Aristotle argued, in his paper "On the Heavens ", that every body has a "heaviness" and so tends to fall to its "natural place". From this he wrongly concluded that an object twice as heavy as another would fall to the ground from the same distance in half the time. Aristotle believed in logic over experimentation and so it wasn't until more than a thousand years later that experiments were developed to prove and disprove laws of mechanics. However, in his "On the Heavens", he made a distinction between "natural motion" and "enforced motion". He led to the conclusion that in avacuum there is no reason for a body to naturally move to one point rather than any other, and so a body in a vacuum will either stay at rest or move indefinitely if put in motion. So Aristotle was really the first to develop the law of inertia. However, when an object is not in a vacuum, he believed that an object would stop moving once the applied forces were removed. The Aristotelians developed elaborate explanations for why an arrow continued to fly through the air once it left the bow - for example, it was proposed that the arrow created a vacuum behind it into which air rushed, providing a force at the back of the arrow. Aristotle's beliefs were based on the fact that the heavens were perfect and had different laws from those on Earth.The

experiment alscientific method was introduced intomechanics in the 11th century byal-Biruni , who along withal-Khazini in the 12th century, unifiedstatics anddynamics into thescience of mechanics, and combined the fields ofhydrostatics with dynamics to create the field ofhydrodynamics . [*Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", in Roshdi Rashed, ed., "*] Early yet incomplete theories pertaining to mechanics were also discovered by several other Muslim physicists during theEncyclopedia of the History of Arabic Science ", Vol. 2, p. 614-642 [642] ,Routledge , London and New YorkMiddle Ages . The law ofinertia , known as Newton's first law of motion, and the concept ofmomentum , part of Newton's second law of motion, were discovered byIbn al-Haytham (Alhacen) [] [Abdus Salam (1984), "Islam and Science". In C. H. Lai (1987), "Ideals and Realities: Selected Essays of Abdus Salam", 2nd ed., World Scientific, Singapore, p. 179-213.*Seyyed*] andHossein Nasr , "The achievements of Ibn Sina in the field of science and his contributions to its philosophy", "Islam & Science", December 2003.Avicenna .Fernando Espinoza (2005). "An analysis of the historical development of ideas about motion and its implications for teaching", "Physics Education"**40**(2), p. 141.] [*Seyyed*] The proportionality betweenHossein Nasr , "Islamic Conception Of Intellectual Life", in Philip P. Wiener (ed.), "Dictionary of the History of Ideas", Vol. 2, p. 65, Charles Scribner's Sons, New York, 1973-1974.force andacceleration , an important principle inclassical mechanics was discovered byHibat Allah Abu'l-Barakat al-Baghdaadi , [*cite encyclopedia*] and theories on gravity were developed by

last =Shlomo Pines

title = Abu'l-Barakāt al-Baghdādī, Hibat Allah

encyclopedia =Dictionary of Scientific Biography

volume = 1

pages = 26-28

publisher = Charles Scribner's Sons

location = New York

date = 1970

isbn = 0684101149

(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", "Journal of the History of Ideas"**64**(4), p. 521-546 [528] .)Ja'far Muhammad ibn Mūsā ibn Shākir , []Robert Briffault (1938). "The Making of Humanity", p. 191.Ibn al-Haytham , [*Nader El-Bizri (2006), "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006), "Medieval Islamic Civilization: An Encyclopaedia", Vol. II, p. 343-345,*] andRoutledge , New York, London.al-Khazini . [*Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", in Roshdi Rashed, ed., "Encyclopaedia of the History of Arabic Science", Vol. 2, p. 622. London and New York: Routledge.*] It is known thatGalileo Galilei 's mathematical treatment ofacceleration and his concept of impetus [*Galileo Galilei, "Two New Sciences", trans. Stillman Drake, (Madison: Univ. of Wisconsin Pr., 1974), pp 217, 225, 296-7.*] grew out of earlier medieval Muslim analyses of motion, especially those ofAvicenna andIbn Bajjah . [*Ernest A. Moody (1951). "Galileo and Avempace: The Dynamics of the Leaning Tower Experiment (I)", "Journal of the History of Ideas"*]**12**(2), p. 163-193.**Isaac Newton**It wasn't until

Galileo Galilei 's development of the telescope and his observations that it became clear that the heavens were not made from a perfect, unchanging substance. FromCopernicus 's heliocentric hypothesis Galileo believed the Earth was just the same as any other planet. Galileo may have performed the famous experiment of dropping two cannon balls from the tower of Pisa. (The theory and the practice showed that they both hit the ground at the same time.) Though the reality of this experiment is disputed, he did carry out quantitative experiments by rolling balls on aninclined plane ; his correct theory of accelerated motion was apparently derived from the results of the experiments. Galileo also found that a body dropped vertically hits the ground at the same time as a body projected horizontally, so an Earth rotating uniformly will still have objects falling to the ground under gravity. More significantly, it showed that uniform motion is indistinguishable from rest, and so forms the basics of the theory of relativity.Sir Isaac Newton was the first to propose and unify all three laws of motion (the law of inertia, his second law mentioned above, and the law of action and reaction), and to prove that these laws govern both everyday objects and celestial objects. Newton and most of his contemporaries, with the notable exception ofChristiaan Huygens , hoped thatclassical mechanics would be able to explain all entities, including (in the form of geometric optics) light. When he discoveredNewton's rings , Newton's own explanation avoided wave principles and, he supposed that the light particles were altered or excited by the glass and resonated.Newton also developed the

calculus which is necessary to perform the mathematical calculations involved in classical mechanics. However it wasGottfried Leibniz who, independently of Newton, developed a calculus with the notation of thederivative andintegral which are used to this day. Newton's dot notation for time derivatives is retained in classical mechanics.**Modern Times**After Newton there were several re-formulations which progressively allowed a solution to be found to a far greater number of problems. The first notable re-formulation was in 1788 by

Joseph Louis Lagrange , an Italian-Frenchmathematician . InLagrangian mechanics the solution is formed through using the path of least action and it is based on theCalculus of variations . Lagrangian mechanics was in turn re-formulated in 1833 byWilliam Rowan Hamilton . The advantage ofHamiltonian mechanics was that its framework allowed for a more in depth look at the underlying principles of classical mechanics. Most of the framework of Hamiltonian mechanics can be seen inQuantum mechanics however the exact meanings of the terms differ due to quantum effects.Although classical mechanics is largely compatible with other "

classical physics " theories such as classicalelectrodynamics andthermodynamics , some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. When combined with classical thermodynamics, classical mechanics leads to theGibbs paradox in whichentropy is not a well-defined quantity. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the energy levels and sizes of atoms. The effort at resolving these problems led to the development ofquantum mechanics . Similarly, the different behaviour of classicalelectromagnetism and classical mechanics under velocity transformations led to thetheory of relativity .By the end of the 20th century, the place of classical mechanics in

physics is no longer that of an independent theory. Along with classicalelectromagnetism , it has become imbedded in relativisticquantum mechanics orquantum field theory ref|Lectures-2-10. It is the non-relativistic, non-quantum mechanical limit for massive particles.Classical mechanics has also been a source of inspiration for mathematicians. The realization was made that the phase space in classical mechanics admits a natural description as a

symplectic manifold (indeed acotangent bundle in most cases of physical interest), andsymplectic topology , which can be thought of as the study of global issues of Hamiltonian mechanics, has been a fertile area of mathematics research starting in the1980s .**Notes****References*** René Dugas "A History of Mechanics" Dover, (1988) ISBN 0-486-65632-2

**ee also***

Mechanics

*Classical mechanics

*Timeline of classical mechanics

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