Project

From Vectorcalcumb

!To Do:

1) Theoretical Background. Define:

Phase Space/Sympletic Manifold (w/ Example)

Symplectic Form

Hamiltonian function

Hamiltonian Vector Field (Xh)

2) Hamilton's Equations

3) Examples:

Free Particle On Line - simple, done in text (pg.70)

Particle on Line: Constant Force

Particle on Line: Linear Spring Force - done in text (pg.70)

Simple pendulum

4) Hamiltonian Flow as level sets of H

The paragraph: "But energy is more than just a conserved quantity: it determines .." (pg.65) (1st page of Chpt 4) is a dramatic pargraph and I like it. We should start out with something of this nature as an opening paragraph. -aaron