We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (qi,pi) to 2N constant values (Q i , P i ), e.g., to the 2N initial values (q i 0 , p i 0) at time t = 0. Then the problem would be solved, q = q(q0,p0,t), P = p(q0,p0,t).
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