Editing Phase space

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]]
@@ Line 1: / Line 1: @@
-'''Phase space''' is the name given to a coordinate-momentum space.
+Phase space is the means by which the mechanical problem is converted in to geometry.
-It is the means by which a mechanical problem can be  converted in to a geometrical problem.
+'''Phase space''', or <math>\Gamma</math>-space, is a 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>
-is the number of [[degree of freedom |degrees of freedom]].
+is the number of degrees of freedom.
-Thus a description of a 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 (known as a ''phase point''). Changes in the 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 (known as a ''phase trajectory'').
+in phase space.
-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.
-==See also==
-*[[Liouville's theorem]]
-*[[H-theorem]]
 [[category: statistical mechanics]]