Editing Configuration space (physics) (section)

==Phase space==
The configuration space is insufficient to completely describe a mechanical system: it fails to take into account velocities.  The set of velocities available to a system defines a plane tangent to the configuration manifold of the system. At a point <math>q\in Q</math>, that tangent plane is denoted by <math>T_q Q</math>. Momentum vectors are linear functionals of the tangent plane, known as cotangent vectors; for a point <math>q\in Q</math>, that cotangent plane is denoted by <math>T^{*}_q Q</math>.  The set of positions and momenta of a mechanical system forms the [[cotangent bundle]] <math>T^*Q</math> of the configuration manifold <math>Q</math>. This larger manifold is called the [[phase space]] of the system.