History of classical mechanics
Encyclopedia
This article deals with the history of classical mechanics
.
, 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 mistakenly claimed that an object twice as heavy as some other would fall to the ground from the same height, in half the time. Aristotle believed in logic and observation but it would be more than a thousand 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 hypothetical vacuum
, there would be no reason for a body to move naturally toward one point rather than any other, and so he concluded a body in a vacuum must either stay at rest or else move indefinitely fast. 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, were individuals come to be and pass away.
Galileo would later observe "the resistance of the air exhibits itself in two ways: first by offering greater impedance to less dense than to very dense bodies, and secondly by offering greater resistance to a body in rapid motion than to the same body in slow motion".
's development of the telescope and his observations that it became clear that the heavens were not made from a perfect, unchanging substance. Adopting Copernicus's heliocentric hypothesis, Galileo believed the Earth was the same as other planets. 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 asserted that uniform motion is indistinguishable from rest, and so forms the basics of the theory of relativity.
Sir 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. 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. Newton's own explanation of Newton's rings
avoided wave principles and 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. Classical mechanics retains Newton's dot notation for time derivatives.
Leonard Euler extended Newton's laws of motion from particles to rigid bodies with two additional laws
.
After Newton, re-formulations progressively allowed solutions to a far greater number of problems. The first was in 1788 by Joseph Louis Lagrange
, an Italian
-French
mathematician
. 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. The advantage of Hamiltonian mechanics
was that its framework allowed a more in–depth look at the underlying principles. 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 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 of quantum mechanics. Similarly, the different behaviour of classical electromagnetism
and classical mechanics under velocity transformations led to the theory of relativity
.
was no longer an independent theory. Along with classical electromagnetism
, it has become imbedded in relativistic
quantum mechanics
or quantum field theory
. It defines 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 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 since the 1980s
.
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
.
Antiquity
The ancient Greek philosophersGreek philosophy
Ancient Greek philosophy arose in the 6th century BCE and continued through the Hellenistic period, at which point Ancient Greece was incorporated in the Roman Empire...
, Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
in particular, were among the first to propose that abstract principles govern nature. Aristotle argued, in On the Heavens
On the Heavens
On the Heavens is Aristotle's chief cosmological treatise: it contains his astronomical theory and his ideas on the concrete workings of the terrestrial world...
, that terrestrial bodies rise or fall to their "natural place" and mistakenly claimed that an object twice as heavy as some other would fall to the ground from the same height, in half the time. Aristotle believed in logic and observation but it would be more than a thousand years before Francis Bacon
Francis Bacon
Francis Bacon, 1st Viscount St Albans, KC was an English philosopher, statesman, scientist, lawyer, jurist, author and pioneer of the scientific method. He served both as Attorney General and Lord Chancellor of England...
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 hypothetical vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
, there would be no reason for a body to move naturally toward one point rather than any other, and so he concluded a body in a vacuum must either stay at rest or else move indefinitely fast. 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, were individuals come to be and pass away.
Galileo would later observe "the resistance of the air exhibits itself in two ways: first by offering greater impedance to less dense than to very dense bodies, and secondly by offering greater resistance to a body in rapid motion than to the same body in slow motion".
Modern Age
It wasn't until Galileo GalileiGalileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
's development of the telescope and his observations that it became clear that the heavens were not made from a perfect, unchanging substance. Adopting Copernicus's heliocentric hypothesis, Galileo believed the Earth was the same as other planets. Galileo may have performed the famous experiment of dropping two cannon balls from the tower of Pisa
Leaning Tower of Pisa
The Leaning Tower of Pisa or simply the Tower of Pisa is the campanile, or freestanding bell tower, of the cathedral of the Italian city 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
Inclined plane
The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
; 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 basics of the theory of relativity.
Sir 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. Newton and most of his contemporaries, with the notable exception of Christiaan Huygens, hoped that classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
would be able to explain all entities, including (in the form of geometric optics) light. Newton's own explanation of Newton's rings
Newton's rings
The phenomenon of Newton's rings, named after Isaac Newton who first studied them in 1717, is an interference pattern caused by the reflection of light between two surfaces - a spherical surface and an adjacent flat surface...
avoided wave principles and supposed that the light particles were altered or excited by the glass and resonated.
Newton also developed the calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
which is necessary to perform the mathematical calculations involved in classical mechanics. However it was Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
who, independently of Newton, developed a calculus with the notation of the derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
and integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
which are used to this day. Classical mechanics retains Newton's dot notation for time derivatives.
Leonard Euler extended Newton's laws of motion from particles to rigid bodies with two additional laws
Euler's laws
Euler's laws of motion, formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws about the motion of particles, extends them to rigid body motion.-Euler's first law:...
.
After Newton, re-formulations progressively allowed solutions to a far greater number of problems. The first was in 1788 by Joseph Louis Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
, an Italian
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
-French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. In Lagrangian mechanics
Lagrangian mechanics
Lagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. It was introduced by the Italian-French mathematician Joseph-Louis Lagrange in 1788....
the solution uses the path of least action
Action (physics)
In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is...
and follows the calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
. William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
re-formulated Lagrangian mechanics in 1833. The advantage of Hamiltonian mechanics
Hamiltonian mechanics
Hamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton.It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without...
was that its framework allowed a more in–depth look at the underlying principles. Most of the framework of Hamiltonian mechanics can be seen in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
however the exact meanings of the terms differ due to quantum effects.
Although classical mechanics is largely compatible with other "classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
" theories such as classical electrodynamics and thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, 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
Gibbs paradox
In statistical mechanics, a semi-classical derivation of the entropy that doesn't take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive...
in which entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
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 of quantum mechanics. Similarly, the different behaviour of classical electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and classical mechanics under velocity transformations led to the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
.
Present
By the end of the 20th century, classical mechanics in physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
was no longer an independent theory. Along with classical electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, it has become imbedded in relativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
or quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
. It defines 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
Phase space
In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space...
in classical mechanics admits a natural description as a symplectic manifold
Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology...
(indeed a cotangent bundle
Cotangent bundle
In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold...
in most cases of physical interest), and symplectic topology
Symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form...
, which can be thought of as the study of global issues of Hamiltonian mechanics, has been a fertile area of mathematics research since the 1980s
1980s
File:1980s decade montage.png|thumb|400px|From left, clockwise: The first Space Shuttle, Columbia, lifted off in 1981; American President Ronald Reagan and Soviet leader Mikhail Gorbachev eased tensions between the two superpowers, leading to the end of the Cold War; The Fall of the Berlin Wall in...
.
See also
- MechanicsMechanicsMechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
- Classical mechanicsClassical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
- Timeline of classical mechanicsTimeline of classical mechanics-Early history:* 300s BC - Aristotle founds the system of Aristotelian physics* 260 BC - Archimedes mathematically works out the principle of the lever and discovers the principle of buoyancy...