Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 8E / a / Solution

The phase space of an $n$-degree-of-freedom mechanical system is the $2n$-dimensional space of canonical positions and momenta $(q_1,\dots ,q_n,p_1,\dots ,p_n)$, geometrically the cotangent bundle of configuration space. A point specifies a complete instantaneous state.