Phase space: Difference between revisions
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Phase space, sometimes written as <math>\Gamma</math>-space, is an Euclidean space in <math>2s</math> dimensions | Phase space, sometimes written as <math>\Gamma</math>-space, is an Euclidean space in <math>2s</math> dimensions | ||
(''i.e.'' <math>E^{2s}</math>), where <math>s</math> | (''i.e.'' <math>E^{2s}</math>), where <math>s</math> | ||
is the number of degrees of freedom. | is the number of [[degree of freedom |degrees of freedom]]. | ||
Thus a description of a system in terms of positions and velocities | Thus a description of a system in terms of positions and velocities | ||
now becomes a point in phase space. Changes in the system now trace out a trajectory | now becomes a point in phase space (known as a ''phase point''). Changes in the system now trace out a trajectory | ||
in phase space. | in phase space (known as a ''phase trajectory''). | ||
Two different phase trajectories cannot pass through the same phase point. | |||
One | One important property of phase space is that, for a long period of time, the phase-trajectory | ||
will spend an equal amount of time in equal volume elements. | will spend an equal amount of time in equal volume elements. | ||
==See also== | ==See also== | ||
Latest revision as of 14:50, 30 July 2008
Phase space is the name given to a coordinate-momentum space. It is the means by which a mechanical problem can be converted in to a geometrical problem. Phase space, sometimes written as -space, is an Euclidean space in dimensions (i.e. ), where is the number of degrees of freedom. Thus a description of a system in terms of positions and velocities now becomes a point in phase space (known as a phase point). Changes in the system now trace out a trajectory in phase space (known as a phase trajectory). Two different phase trajectories cannot pass through the same phase point. One important property of phase space is that, for a long period of time, the phase-trajectory will spend an equal amount of time in equal volume elements.
