For a particle moving under a central potential centred on the origin

PHYSICS · Subjective · 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

For a particle moving under a central potential centred on the origin, the xx-component of angular momentum, G=Lx=ypz−zpyG=L_x=yp_z-zp_y, is a conserved quantity. At an instant when the particle is at r=(0, 2.0, 0) m\mathbf r=(0,\,2.0,\,0)\,\mathrm m with momentum p=(0, 0, 3.0) kg m s−1\mathbf p=(0,\,0,\,3.0)\,\mathrm{kg\,m\,s^{-1}}, compute the infinitesimal canonical transformation generated by GG with ϵ=0.020 rad\epsilon=0.020\,\mathrm{rad}, and identify the symmetry it produces.

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