# Solve non-dimensionalized spring pendulum system on python

1. Dec 4, 2013

### gothloli

1. The problem statement, all variables and given/known data
I'm supposed to solve the spring pendulum numerically on python 2.7, using odeint. The system is supposed to solved for the y -direction and the x-direction in terms of time. In class we did this for pendulum DE, but that only had x as the dependent variable, this system has two.

2. Relevant equations
These are the non-dimensionalized De's I get
$\frac{d^{2}Y}{d\tau^{2}} = -1+\frac{(1-Y)}{\sigma}-\frac{(1-\sigma)(1-Y)}{\sigma\sqrt{X^{2}+(1-Y)^{2}}}$

and
$\frac{d^{2}X}{d\tau^{2}}=-\frac{X}{\sigma}+\frac{(1-\sigma)X}{\sigma\sqrt{X^{2}+(1-Y)^{2}}}$.
Where σ is the non-dimensional parameter

3. The attempt at a solution
def rhs(xvector,t):

x1dot=xvector[1]
x2dot=xvector[3]
x3dot=yvector[0]
x4dot=(-xvector[1]/sigma)+((1-sigma)*xvector[0])/(sigma*sqrt((xvector[0])**2+(1-yvector[0])**2))

return [x1dot,x2dot,x3dot,x4dot]

This is the beginning of the code, but I don't know how to include the y vector into this function?

Last edited: Dec 4, 2013