Configuration space: Encyclopedia - Configuration space

Configuration space

In classical mechanics, the configuration space is the space of possible positions that a physical system may attain, possibly subject to external constraints. The configuration space of a typical system has the structure of a manifold; for this reason it is also called the configuration manifold.

For example, the configuration space of a single particle moving in ordinary Euclidean 3-space is just R³. For N particles the configuration space is R^3N, or possibly the subspace where no two positions were equal. More generally, one can regard the configuration space of N particles moving in a manifold M as the function space M^N.

To take account of both position and momenta one moves to the cotangent bundle of the configuration manifold. This larger manifold is called the phase space of the system. In short, a configuration space is typically "half" of (see Lagrangian distribution) a phase space that is constructed from a function space.

In quantum mechanics one formulation emphasises 'histories' as configurations.

Configuration spaces are related to braid theory, also, since the condition on a string of not passing through itself is formulated by cutting diagonals out of function spaces.

See also

• phase space
• function space

Category: Classical mechanics

Adapted from the Wikipedia article "Configuration space", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki