Configuration space Given a topological space
, the
th ordered configuration space of
denoted by
is the set of
-tuples of pairwise distinct points in
, that is
.
In physics, parameters are used to define the configuration of a system and the vector space defined by these parameters is the configuration space of the system. It is used to describe the state of a whole system as a single point in a higher-dimensional space.
Examples of Configuration space
1. The configuration space of a particle in
is
. For
particles in
, it is
2. For a rigid body in
, the configuration space is
. Generally, it is
, where
is the special orthogonal group.
3. The torus with its diagonal removed,
, is the configuration space of two points on
. This is
Reference: [1]