Classical mechanics
From ePedia, the electronic encyclopedia
In physics, classical mechanics or Newtonian mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies. The other sub-field is quantum mechanics. The term classical mechanics was coined in the early 20th century to describe the system of mathematical physics developed in the 400 years since the groundbreaking works of Brahe, Kepler, and Galileo, but before the development of quantum physics. Quantum physics (and more specifically quantum mechanics) refers to developments since approximately 1900, starting with similarly decisive discoveries by Planck, Einstein, and Bohr. The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the mathematical methods invented by Newton himself, in parallel with Leibniz, and others. This is further described in the following sections. More abstract, and general methods include Lagrangian mechanics and Hamiltonian mechanics. While the terms classical mechanics and Newtonian mechanics are usually considered equivalent, the conventional content of classical mechanics was created in the 19th century and differs considerably (particularly in its use of analytical mathematics) from the work of Newton.
Classical mechanics produces very accurate results within the domain of everyday experience. It is enhanced by special relativity for objects moving with high velocity, more than about a third the speed of light. Classical mechanics is used to describe the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies, and even microscopic objects such as large molecules. Besides this, many specialties exist, dealing with gases, liquids, and solids, and so on. It is one of the largest subjects in science and technology.
Description of the theory
The following introduces the basic concepts of classical mechanics. For simplicity, it uses point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it. Each of these parameters is discussed in turn.
In reality, the kind of objects which classical mechanics can describe always have a non-zero size. True point particles, such as the electron, are normally better described by quantum mechanics. Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.
Position and its derivatives
The position of a point particle is defined with respect to an arbitrary fixed point in space, which is sometimes called the origin, O. It is defined as the vector r from O to the particle. In general, the point particle need not be stationary, so r is a function of t, the time elapsed since an arbitrary initial time. In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute in all reference frames. In addition to relying on absolute time, classical mechanics uses Euclidean geometry.
Classical mechanics produces very accurate results within the domain of everyday experience. It is enhanced by special relativity for objects moving with high velocity, more than about a third the speed of light. Classical mechanics is used to describe the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies, and even microscopic objects such as large molecules. Besides this, many specialties exist, dealing with gases, liquids, and solids, and so on. It is one of the largest subjects in science and technology.
Description of the theory
The following introduces the basic concepts of classical mechanics. For simplicity, it uses point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it. Each of these parameters is discussed in turn.
In reality, the kind of objects which classical mechanics can describe always have a non-zero size. True point particles, such as the electron, are normally better described by quantum mechanics. Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.
Position and its derivatives
The position of a point particle is defined with respect to an arbitrary fixed point in space, which is sometimes called the origin, O. It is defined as the vector r from O to the particle. In general, the point particle need not be stationary, so r is a function of t, the time elapsed since an arbitrary initial time. In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute in all reference frames. In addition to relying on absolute time, classical mechanics uses Euclidean geometry.
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