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Revision as of 01:47, 2 May 2006 (edit) 69.173.27.2 (Talk) ← Previous diff		Current revision as of 00:10, 3 May 2006 (edit) (undo) Aaronwelles (Talk | contribs)
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Line 1:		Line 1:
-	To Do:	+	!To Do:
-	1) Theoretical Background
-	Define:
-	Symplectic Form
-	Hamiltonian function
-	Vector Field Xh
-	Phase Space (w/ Example)
-	2) Hamiltonian Functions	+	1) Theoretical Background. Define:
		+
		+	[[Phase Space/Sympletic Manifold]] (w/ Example)
		+
		+	[[Symplectic Form]]
		+
		+	[[Hamiltonian function]]
		+
		+	[[Hamiltonian Vector Field (Xh)]]
		+
		+
		+	2) [[Hamilton's Equations]]
		+
	3) Examples:		3) Examples:
-	Free Particle	+
-	Linear Motion (?)	+	[[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		Simple pendulum
		+
	4) Hamiltonian Flow as level sets of H		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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Current revision as of 00:10, 3 May 2006

!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