Editing Project

To Do:


1) Theoretical Background. Define:

Symplectic Form

Hamiltonian function

Vector Field Xh

Phase Space (w/ Example)


2) Hamiltonian Functions


3) Examples:

Free Particle

Linear Motion (?)

Simple pendulum


4) Hamiltonian Flow as level sets of H
@@ Line 1: / Line 1: @@
-!To Do:
+To Do:
 ) Theoretical Background. Define:
-[[Phase Space/Sympletic Manifold]] (w/ Example)
+Symplectic Form
-[[Symplectic Form]]
+Hamiltonian function
-[[Hamiltonian function]]
+Vector Field Xh
-[[Hamiltonian Vector Field (Xh)]]
+Phase Space (w/ Example)
-) [[Hamilton's Equations]]
+) Hamiltonian Functions
 ) Examples:
-[[Free Particle On Line]] - simple, done in text (pg.70)
+Free Particle
-[[Particle on Line: Constant Force]]
+Linear Motion (?)
-Particle on Line: Linear Spring Force - done in text (pg.70)
 Simple pendulum
@@ Line 28: / Line 26: @@
 ) 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