Problem 3: Start with the Lagrangian to setup the Hamiltonian for "Simple Pendulum" and determine 0 for the pendulum bob by writing down the Hamilton's equations of motion. There is no need to solve this equation. Also write down the Hamilton-Jacobi equation of motion for this system by using the generating function S(q, P, t). There is no need to solve the resulting partial differential equation.
Problem 3: Start with the Lagrangian to setup the Hamiltonian for "Simple Pendulum" and determine 0 for the pendulum bob by writing down the Hamilton's equations of motion. There is no need to solve this equation. Also write down the Hamilton-Jacobi equation of motion for this system by using the generating function S(q, P, t). There is no need to solve the resulting partial differential equation.
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