Phase space - Revision history

Carl McBride: Added an internal link.

2008-07-30T13:50:28Z

Added an internal link.

← Older revision		Revision as of 15:50, 30 July 2008
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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 (known as a ''phase point''). 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

Carl McBride at 12:33, 22 August 2007

2007-08-22T12:33:12Z

← Older revision		Revision as of 14:33, 22 August 2007
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	is the number of degrees of freedom.		is the number of 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 ~~of the most~~ important ~~properties~~ of phase space is that, for a long period of time, the phase-trajectory		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==

Carl McBride at 10:41, 3 August 2007

2007-08-03T10:41:39Z

← Older revision		Revision as of 12:41, 3 August 2007
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	Phase space is the means by which ~~the~~ mechanical problem is converted in to ~~geometry~~.		'''Phase space''' is the name given to a coordinate-momentum space.
	~~'''~~Phase space~~'''~~, or <math>\Gamma</math>-space, is a Euclidean space in <math>2s</math> dimensions		It is the means by which a mechanical problem can be converted in to a geometrical problem.
			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 degrees of freedom.
	Thus ~~our~~ description of ~~our~~ 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 ~~our~~ system now trace out a trajectory		now becomes a point in phase space. Changes in the system now trace out a trajectory
	in phase space.		in phase space.

			One of the most important properties 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.
			==See also==
			*[[Liouville's theorem]]
			*[[H-theorem]]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride at 13:07, 5 July 2007

2007-07-05T13:07:56Z

← Older revision		Revision as of 15:07, 5 July 2007
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	Thus our description of our system in terms of positions and velocities		Thus our description of our system in terms of positions and velocities
	now becomes a point in phase space. Changes in our system now trace out a trajectory		now becomes a point in phase space. Changes in our system now trace out a trajectory
	in phase space. ~~xx3xx~~		in phase space.
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride at 13:07, 5 July 2007

2007-07-05T13:07:44Z

← Older revision		Revision as of 15:07, 5 July 2007
Line 5:		Line 5:
	Thus our description of our system in terms of positions and velocities		Thus our description of our system in terms of positions and velocities
	now becomes a point in phase space. Changes in our system now trace out a trajectory		now becomes a point in phase space. Changes in our system now trace out a trajectory
	in phase space.		in phase space. xx3xx
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride: New page: Phase space is the means by which the mechanical problem is converted in to geometry. '''Phase space''', or $\Gamma$ -space, is a Euclidean space in $2s$ dimensions (...

2007-05-29T09:15:41Z

New page: Phase space is the means by which the mechanical problem is converted in to geometry. '''Phase space''', or <math>\Gamma</math>-space, is a Euclidean space in <math>2s</math> dimensions (...

New page

Phase space is the means by which the mechanical problem is converted in to geometry.
'''Phase space''', or <math>\Gamma</math>-space, is a Euclidean space in <math>2s</math> dimensions
(''i.e.'' <math>E^{2s}</math>), where <math>s</math>
is the number of degrees of freedom.
Thus our description of our system in terms of positions and velocities
now becomes a point in phase space. Changes in our system now trace out a trajectory
in phase space.
[[category: statistical mechanics]]

Phase space - Revision history

Carl McBride: Added an internal link.

Carl McBride at 12:33, 22 August 2007

Carl McBride at 10:41, 3 August 2007

Carl McBride at 13:07, 5 July 2007

Carl McBride at 13:07, 5 July 2007

Carl McBride: New page: Phase space is the means by which the mechanical problem is converted in to geometry. '''Phase space''', or \Gamma-space, is a Euclidean space in 2s dimensions (...

Carl McBride: New page: Phase space is the means by which the mechanical problem is converted in to geometry. '''Phase space''', or $\Gamma$ -space, is a Euclidean space in $2s$ dimensions (...