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单词 phase space
释义

phase space


phase space

n. A multidimensional representation of a dynamical system in which each dimension corresponds to one variable of the system. Thus, a point of phase space corresponds to a specific state of the system, and a path represents the evolution of the system through different states.
Thesaurus
Noun1.phase space - (physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance; "a multidimensional phase space"infinite, space - the unlimited expanse in which everything is located; "they tested his ability to locate objects in space"; "the boundless regions of the infinite"natural philosophy, physics - the science of matter and energy and their interactions; "his favorite subject was physics"dynamical system - (physics) a phase space together with a transformation of that space
Translations
spazio delle fasi

Phase Space


phase space

[′fāz ‚spās] (mathematics) In a dynamical system or transformation group, the topological space whose points are being moved about by the given transformations. (statistical mechanics) For a system with n degrees of freedom, a euclidean space with 2 n dimensions, one dimension for each of the generalized coordinates and one for each of the corresponding momenta.

Phase Space

 

in classical and statistical mechanics, the multidimensional space of all generalized coordinates qi and generalized momenta pi (i = 1, 2,. .., N) of a mechanical system with N degrees of freedom. Thus, phase space has 2N dimensions and may be described by means of an orthogonal coordinate system with 2N axes; the number of axes corresponds to the number of generalized coordinates and momenta.

The state of a system is represented in phase space by a point with the coordinates q1, p1, . . ., qN, pN. A change in the state of the system with time is represented by the motion of the point along a line called a phase trajectory. For phase space, the concept of phase volume and other concepts in multidimensional geometry can be introduced.

Phase space is a fundamental concept in classical statistical mechanics, which studies the distribution functions of systems of many particles. Phase-space methods are also used in the theory of nonlinear oscillations.

Phase space


Phase space

A graph which shows all possible states of a system. In phase space we plot the value of a variable against possible values of the other variables at the same time. If a system had three descriptive variables, we plot the phase space in three dimensions, with each variable taking one dimension.

phase space


Related to phase space: Liouville's theorem
  • noun

Words related to phase space

noun (physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance

Related Words

  • infinite
  • space
  • natural philosophy
  • physics
  • dynamical system
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更新时间:2025/2/24 7:26:07