Introduction

In this lab you will discover another connection between gradient and Hamiltonian vector fields. In particular, you will show how the the motion of a particle under the influence of a one-dimensional gradient force field gives rise to a two-dimensional Hamiltonian phase space vector field.

You will need to invoke Maple for this lab. Include the two standard packages

with(plots): with(DEtools):

Outline

• One dimensional gradient motion.
• The motion in phase space.
• By George, it's Hamiltonian!
• Hamiltonian systems and energy.