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Initial Conditions Applied to a Lagrangian

  1. Feb 22, 2016 #1
    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. jcsd
  3. Feb 22, 2016 #2

    BvU

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    Hello vs, :welcome:

    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 :smile: ).
     
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