Lesson 17
Hamiltonian Dynamics

1) You can probably see that there are certain steps required in order to be able to determine the Hamilton's equations of motion for a particular system. Make a list (number the steps) explaining what you think the steps are that would take you along the route to the Hamilton's equations of motion for any specific problem. Your list should be a step-by-step to-do list.

2) Estimate a numerical value for the Hamiltonian for a grade school child swinging on a backyard swing. (Don't forget to explain your assumptions and estimates!)

3) Which of the following statements about Hamilton's equations of motion is true?

1. They are coupled first order differential equations, unlike the second order equations yielded by both Newton II and the Lagrangian formulation.
2. They are equations based on the Hamiltonian, which is a conserved quantity that equals the total energy T+U of the system.
3. There are the same number of Hamilton's equations of motion (or 'canonical equations of motion') for a given system as there are Lagrange equations to describe that same system.
4. For a given system, the Hamilton's equations of motion are easier to obtain than the Lagrange equations.

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