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!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

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