A particle of mass kg moves without friction in a vertical plane under uniform gravity
PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Hamiltonian mechanics and canonical structure · Hamiltonian mechanics and canonical structure
Action and Symmetry, Ch Hamilton-Jacobi theory and action-angle variables
Problem
A particle of mass m=0.50 kg moves without friction in a vertical plane under uniform gravity g=9.8ms−2, with horizontal coordinate x and height z. No other forces act.
((a)) Write the Hamiltonian and the Hamilton-Jacobi equation for Hamilton's principal function S(x,z,t).
((b)) State how many independent non-additive constants a complete solution must contain, and give a physical name for two such constants for this system.