# Initial Conditions Applied to a Lagrangian

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1. Feb 22, 2016

### vs74043

1. The problem statement, all variables and given/known data

The scenario is a pendulum of length l and mass m2 attached to a mass of m1 which is allowed to slide along the horizontal with no friction. The support mass moves along in the X direction and the pendulum swings through the x-y plane with an angle θ with the vertical. After finding the Lagrangian and the Euler-Lagrange equations for each of the two variables X and θ, apply the conditions
$$\theta(0)=\theta_{0}<<1\text{ but greater than 0}\\ \dot{\theta}(0)=0\\ X(0)=0\\ \dot{X}(0)=0$$
to get the motion for θ and X.
2. Relevant equations
I have derived the Lagrangian of this to be
$$L=\frac{1}{2}(m_{1}+m_{2})\dot{X}^{2}+m_{2}l\cos\theta\dot{\theta}\dot{X}+\frac{1}{2}m_{2}l^{2}\dot{\theta}^{2}+m_{2}gl\cos\theta$$

3. The attempt at a solution

Last edited: Feb 22, 2016
2. Feb 22, 2016

### BvU

Hello vs,

Post needs some adjusting to the PF guidelines. What relevant equations do you have to continue this exercise ? What you mention now is an intermediate result (which I think is right, but I didn't check it - will do so if you show the steps ).