(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Classical Mechanics: Canonical transformation problem

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