TI-89 Hamiltonian Finder version 1
(C) 2000 Bennett S. Kalafut

INSTALLATION:

This function may be installed to any folder on you TI-89.


OVERVIEW:

Given a two equation first order system of differential equations, fuction Hamilton will test if it is Hamiltonian.  If it is, Hamilton will return the Hamiltonian function for the system.  If not, Hamilton will return "The system is not Hamiltonian."


WHAT IS A HAMILTONIAN?:
A system of differential equations x' and y' is Hamiltonian if there is some function H(x,y) which has constant value over the solutions of the system.

It is formally defined as follows:

A system of differential equations x' and y' is called a Hamiltonian system if there exists a real-valued function H(x,y) such that

	x'=the partial derivative of H with respect to y
	y'=-1*the partial derivative of H with respect to x

for all x and y.  The function H is called the Hamiltonian Function for the system.

Note that any solution curve of the system in the phase plane will be a level curve of the Hamiltonian.

You may also determine if there is a conserved quantity in a second order equation.  Set y' equal to v and v' equal to y''.  You may use this program to, for example, find the energy function of an undamped harmonic oscillator.

SYNTAX:
hamiltonian(x',y',varlist)
x',y' being the differential equations of the system
varlist being the names of the variables, as a list (for example, {x,y}.)


CONTACT INFORMATION:

To report any bugs or to suggest any improvements, e-mail me at bkalafut@bigfoot.com


LICENSE:

You are licensed to freely distribute this (TI-89 Hamiltonian Finder) product as long as this text file is distributed with it and the recipient of the product pays no fee.

You may include the code of this product into your own programs, provided that I am given credit for the authoring of that segment of code.

You may NOT
1) Charge a fee for the distribution of this product.
2) Include this product in any printed book of programs without my written permission.

Use of the product implies acceptance of these terms.