Mechanical configuration space ($Q$)

The configuration space of a mechanical system is the space of its allowed positions or generalized coordinates. Its tangent bundle describes configurations and velocities, and its cotangent bundle describes configurations and conjugate momenta. For smooth holonomic constraints it is a manifold on which geometric Lagrangian and Hamiltonian descriptions can be built. Singular constraints or symmetry quotients can require strata rather than one global smooth manifold.

A mechanical configuration specifies the positions and orientations of all parts of a system, subject to its constraints. It is a point of the mechanical configuration space $Q$; generalized coordinates label such points locally. A configuration does not by itself specify velocities, so it generally does not determine the system's full dynamical state. For a bead on a fixed circular hoop, its angle specifies its configuration, while its angular velocity is additional data.