Classical mechanics  
History of ...


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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 a vacuum 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 experimental scientific method was introduced into mechanics in the 11th century by alBiruni, who along with alKhazini in the 12th century, unified statics and dynamics into the science of mechanics, and combined the fields of hydrostatics with dynamics to create the field of hydrodynamics.^{[1]} Early yet incomplete theories pertaining to mechanics were also discovered by several other Muslim physicists during the Middle Ages. The law of inertia, known as Newton's first law of motion, and the concept of momentum, part of Newton's second law of motion, were discovered by Ibn alHaytham (Alhacen)^{[2]}^{[3]} and Avicenna.^{[4]}^{[5]} The proportionality between force and acceleration, an important principle in classical mechanics was discovered by Hibat Allah Abu'lBarakat alBaghdaadi,^{[6]} and theories on gravity were developed by Ja'far Muhammad ibn Mūsā ibn Shākir,^{[7]} Ibn alHaytham,^{[8]} and alKhazini.^{[9]} It is known that Galileo Galilei's mathematical treatment of acceleration and his concept of impetus^{[10]} grew out of earlier medieval Muslim analyses of motion, especially those of Avicenna^{[4]} and Ibn Bajjah.^{[11]}
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. From Copernicus'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 an inclined 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 of Christiaan Huygens, hoped that classical mechanics would be able to explain all entities, including (in the form of geometric optics) light. When he discovered Newton'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 was Gottfried Leibniz who, independently of Newton, developed a calculus with the notation of the derivative and integral which are used to this day. Newton's dot notation for time derivatives is retained in classical mechanics.
Leonard Euler extended Newton's laws of motion from particles to rigid bodies with two additional laws.
After Newton there were several reformulations which progressively allowed a solution to be found to a far greater number of problems. The first notable reformulation was in 1788 by Joseph Louis Lagrange, an ItalianFrench mathematician. In Lagrangian mechanics the solution is formed through using the path of least action and it is based on the Calculus of variations. Lagrangian mechanics was in turn reformulated in 1833 by William Rowan Hamilton. The advantage of Hamiltonian 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 in Quantum 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 classical electrodynamics and thermodynamics, 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 the Gibbs paradox in which entropy is not a welldefined 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 of quantum mechanics. Similarly, the different behaviour of classical electromagnetism and classical mechanics under velocity transformations led to the theory 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 classical electromagnetism, it has become imbedded in relativistic quantum mechanics or quantum field theory^{[1]}. It is the nonrelativistic, nonquantum 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 a cotangent bundle in most cases of physical interest), and symplectic 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 the 1980s.
