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 q ∈ ∈ Q , that tangent plane is denoted by T q Q . Momentum vectors are linear functionals of the tangent plane, known as cotangent vectors; for a point q ∈ ∈ Q , that cotangent plane is denoted by T q ∗ ∗ Q . The set of positions and momenta of a mechanical system forms the cotangent bundle T ∗ ∗ Q of the configuration manifold Q . This larger manifold is called the phase space of the system.