A change of phase-space variables is proposed as ,

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Hamiltonian mechanics and canonical structure · Hamiltonian mechanics and canonical structure

Action and Symmetry, Ch Canonical transformations, generating functions and symplectic structure

Problem

A change of phase-space variables is proposed as Q=q3Q = q^3, P=p/(3q2)P = p/(3q^2), valid for q≠0q \neq 0, with qq in m\mathrm{m} and pp in kg m s−1\mathrm{kg\,m\,s^{-1}}. ((a)) Compute {Q,P}\{Q,P\} using the definitions in (q,p)(q,p). ((b)) State whether the transformation is canonical.

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