What Is Phase Space

This section provides a quick introduction to Phase Space, which is the collection of all possible sets of canonical coordinates (q,p) of a system.

What Is Phase Space? Phase Space is the collection of all possible sets of canonical coordinates of a system.

What Are Canonical Coordinates? Canonical Coordinates are generalized position components, qi, extended with generalized momentum components pi.

In other words, a point in Phase Space is a set of canonical coordinates with components of q1, q2, ..., p1, p2, ....

A point in Phase Space is also called the state of the system at a given time instance.

For a single-object system with 1 degree of freedom, the Phase Space is a 2 dimensional space of (q1, p1). In this case, the Phase Space is called Phase Plane.

For a single-object system with 2 degree of freedom, the Phase Space is a 4 dimensional space of (q1, q2, p1, p2).

Note that some text books define Phase Space as the collection of all possible sets of generalized position components qi, with generalized velocity components q'i.

The difference is only a factor of mass, m, in most cases, because of the following relations.

```pi = m*q'i
```