# hemn space

Configuration space

In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system. It is often the case that these parameters satisfy mathematical constraints, which means that the set of actual configurations of the system is a manifold in the space of generalized coordinates. This manifold is called the configuration manifold of the system.

Configuration spaces in physics

The configuration space of a single particle moving in ordinary Euclidean 3-space is just R3. For n particles the configuration space isR3n, or possibly the subspace where no two positions are equal. More generally, one can regard the configuration space of n particles moving in a manifold M as the function space Mn.

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 spacethat is constructed from a function space.

In quantum mechanics one formulation emphasises ‘histories’ as configurations.