1. The problem statement, all variables and given/known data Show directly that the transformation; Q=log(1/q*sinp), P=q*cotp is canonical. 2. Relevant equations Since these equations have no time dependence, the equations are canonical if (with d denoting a partial derivative) dQ_i/dq_j = dp_j/dP_i, and dQ_i/dp_j = -dq_j/dP_i 3. The attempt at a solution With Q=log(1/q*sinp), dQ/dq = -1/q P=q*cotp => p=tan^-1(q/P), dp/dP = -q/(p^2+q^2). The first problem I encounter is that -1/q not= -q/(p^2+q^2). With dQ/dp = cotp, and -dq/dP = -1/(dP/dq) = -cotp so, cotp not= -cotp.