We construct a Cartesian space in which each of the \(6N\) coordinates and momenta is assigned to one of \(6N\) mutually orthogonal axes. Phase space is, therefore, a \(6N\) dimensional space. A point in this space is specified by giving a particular set of values for the \(6N\) coordinates and momenta. Denote such a point by \[ x = (p_1, \cdots , p_N, r_1, \cdots , r_N ) \nonumber \] \(x\) is a \(6N\) dimensional vector. Thus, the time evolution or trajectory of a system as specified by Hamilton's equations of motion, can be expressed by giving the phase space vector, \(x\) as a function of time. The law of conservation of energy, expressed as a condition on the phase space vector: \[ H(x(t)) = \text {const} = E \nonumber \] defines a \(6N - 1\) dimensional hypersurface in phase space on which the trajectory must remain.