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 (see history of thermodynamics) and electromagnetism (see history of electromagnetism).
The critical historical event in classical mechanics was the publication by Isaac Newton of his laws of motion and his associated development of the mathematical techniques of calculus in 1678. Analytic tools of mechanics grew through the next two centuries, including the development of Hamiltonian mechanics and the action principles, concepts critical to the development of quantum mechanics and of relativity.
Chaos theory is a subfield of classical mechanics that was developed in its modern form in the 20th century.
Precursors to Newtonian mechanics
Antiquity
The ancient Greek philosophers, Aristotle in particular, were among the first to propose that abstract principles govern nature. Aristotle argued, in On the Heavens, that terrestrial bodies rise or fall to their "natural place" and stated as a law the correct approximation that an object's speed of fall is proportional to its weight and inversely proportional to the density of the fluid it is falling through. Aristotle believed in logic and observation but it would be more than eighteen hundred years before Francis Bacon would first develop the scientific method of experimentation, which he called a vexation of nature.
Aristotle saw a distinction between "natural motion" and "forced motion", and he believed that 'in a void' i.e.vacuum, a body at rest will remain at restAristotle: On the Heavens (de Caelo) book 13, section 295a and a body in motion will continue to have the same motion.Aristotle:Physics Book 4 On motion in a void In this way, Aristotle was the first to approach something similar to the law of inertia. However, he believed a vacuum would be impossible because the surrounding air would rush in to fill it immediately. He also believed that an object would stop moving in an unnatural direction once the applied forces were removed. Later Aristotelians developed an elaborate explanation for why an arrow continues to fly through the air after it has left the bow, proposing that an arrow creates a vacuum in its wake, into which air rushes, pushing it from behind. Aristotle's beliefs were influenced by Plato's teachings on the perfection of the circular uniform motions of the heavens. As a result, he conceived of a natural order in which the motions of the heavens were necessarily perfect, in contrast to the terrestrial world of changing elements, where individuals come to be and pass away.
There is another tradition that goes back to the ancient Greeks where mathematics is used to analyze bodies at rest or in motion, which may found as early as the work of some Pythagoreans. Other examples of this tradition include Euclid (On the Balance), Archimedes (On the Equilibrium of Planes, On Floating Bodies), and Hero (Mechanica). Later, Islamic and Byzantine scholars built on these works, and these ultimately were reintroduced or became available to the West in the 12th century and again during the Renaissance.
Medieval thought Persian Islamic polymath Ibn Sīnā published his theory of motion in The Book of Healing (1020). He said that an impetus is imparted to a projectile by the thrower, and viewed it as persistent, requiring external forces such as air resistance to dissipate it. Ibn Sina made distinction between 'force' and 'inclination' (called "mayl"), and argued that an object gained mayl when the object is in opposition to its natural motion. So he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the mayl is spent. He also claimed that projectile in a vacuum would not stop unless it is acted upon. This conception of motion is consistent with Newton's first law of motion, inertia. Which states that an object in motion will stay in motion unless it is acted on by an external force.Espinoza, Fernando. "An Analysis of the Historical Development of Ideas About Motion and its Implications for Teaching". Physics Education. Vol. 40(2).
In the 12th century, Hibat Allah Abu'l-Barakat al-Baghdaadi adopted and modified Avicenna's theory on projectile motion. In his Kitab al-Mu'tabar, Abu'l-Barakat stated that the mover imparts a violent inclination (mayl qasri) on the moved and that this diminishes as the moving object distances itself from the mover. According to Shlomo Pines, al-Baghdaadi's theory of motion was "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]."(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", Journal of the History of Ideas 64 (4), p. 521-546 .)
In the 14th century, French priest Jean Buridan developed the theory of impetus, with possible influence by Ibn Sina.Sayili, Aydin. "Ibn Sina and Buridan on the Motion the Projectile". Annals of the New York Academy of Sciences vol. 500(1). p.477-482. Albert, Bishop of Halberstadt, developed the theory further.
Nicole Oresme, one of Oxford Calculators at Merton College, Oxford, provided the mean speed theorem using geometrical arguments.
Galileo and Huygens
Galileo Galilei's development of the telescope and his observations further challenged the idea that the heavens were made from a perfect, unchanging substance. Adopting Copernicus's heliocentric hypothesis, Galileo believed the Earth was the same as other planets. Though the reality of the famous Tower of Pisa 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 asserted that uniform motion is indistinguishable from rest, and so forms the basis of the theory of relativity. Except with respect to the acceptance of Copernican astronomy, Galileo's direct influence on science in the 17th century outside Italy was probably not very great. Although his influence on educated laymen both in Italy and abroad was considerable, among university professors, except for a few who were his own pupils, it was negligible."Galilei, Galileo." Complete Dictionary of Scientific Biography. Retrieved April 06, 2021 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/galilei-galileo
Christiaan Huygens was the foremost mathematician and physicist in Western Europe. He formulated the conservation law for elastic collisions, produced the first theorems of centripetal force, and developed the dynamical theory of oscillating systems. He also made improvements to the telescope, discovered Saturn's moon Titan, and invented the pendulum clock.
Newtonian mechanics Isaac Newton was the first to unify the 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 earthly and celestial objects in 1687 in his treatise Philosophiæ Naturalis Principia Mathematica. Newton and most of his contemporaries hoped that classical mechanics would be able to explain all entities, including (in the form of geometric optics) light.
Newton's work was more than a mere synthesis of previous results; rather, Newton carefully selected and fundamentally transformed concepts, principles, laws, and hypotheses from his predecessors. This creative process resulted in a new form for each idea. He approached natural philosophy with mathematics in a completely novel way, in that instead of a preconceived natural philosophy, his style was to begin with a mathematical construct, and build on from there, comparing it to the real world to show that his system accurately accounted for it.
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. Classical mechanics retains Newton's dot notation for time derivatives.
Leonhard Euler extended Newton's laws of motion from particles to rigid bodies with two additional laws. Working with solid materials under forces leads to deformations that can be quantified. The idea was articulated by Euler (1727), and in 1782 Giordano Riccati began to determine elasticity of some materials, followed by Thomas Young. Simeon Poisson expanded study to the third dimension with the Poisson ratio. Gabriel Lamé drew on the study for assuring stability of structures and introduced the Lamé parameters.Gabriel Lamé (1852) Leçons sur la théorie mathématique de l'élasticité des corps solides (Bachelier) These coefficients established linear elasticity theory and started the field of continuum mechanics.
Analytical mechanics
After Newton, re-formulations progressively allowed solutions to a far greater number of problems. The first was constructed in 1788 by Euler and Joseph Louis Lagrange. In Lagrangian mechanics the solution uses the path of least action and follows the calculus of variations. William Rowan Hamilton re-formulated Lagrangian mechanics in 1833, resulting in Hamiltonian mechanics. In addition to the solutions of important problems in classical physics, these techniques form the basis for quantum mechanics: Lagrangian methods evolved in to the path integral formulation and the Schrödinger equation builds Hamiltonian mechanics.
In the middle of the 19th century, Hamilton could claim classical mechanics as at the center of attention among scholars: Between 1860 and 1877 Edward Routh introduced a method to reduce variables which influenced stability theory and control theory. In 1877, he presented the Routhian, a hybrid between the Lagrangian and the Hamiltonian.
Origin of chaos theory In the 1880s, while studying the three-body problem, Henri Poincaré found that there can be orbits that are nonperiodic, and yet not forever increasing nor approaching a fixed point. In 1898, Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature, called Hadamard's billiards. Hadamard was able to show that all trajectories are unstable, in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent.
These developments led in the 20th century to the development of chaos theory.
Conflicts at the end of the 19th century