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# Phase space

**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.