# Lagrangian problem setup question.

1. Mar 24, 2012

### djones64

1. The problem statement, all variables and given/known data
Consider a particle of mass m moving in a vertical x-y plane along a curve y = a*cos((2$\pi$x)/$\lambda$). Consider its motion in terms of two coordinates x and y.
Find Lagrange's equations of motion with undetermined multipliers.

2. Relevant equations
y = a*cos((2$\pi$x)/$\lambda$);
(partial L/partial x) - d/dt(partial L/partial x dot) + $\lambda$*(partial L/partial x) (sorry, couldn't figure out how to write the formula)

3. The attempt at a solution
All problems that we have been given of this type have had two independent equations for x and y. In this one y depends on x. I attempted to use the parameters x=x and $\dot{x}$=$\dot{x}$. The calculations are too long to post, but the answer I am getting for x double dot is crazy. I can see from the picture that y=a at x=0 and at x=$\lambda$. Is there a way to use that to get my independent x parameter? If this problem belongs in the advanced physics forum, please let me know. Thank you in advance.

#### Attached Files:

• ###### 2012-03-23_20-44-45_735.jpg
File size:
18.9 KB
Views:
50
Last edited: Mar 24, 2012