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Euler Lagrange equations with viscous dissipation

  1. Sep 30, 2014 #1
    1. The problem statement, all variables and given/known data
    The system can pivot at point O and I am taking small angle approximations.
    I am trying to determine the Lagrangian, ##\mathcal{L} = T - U## for the following system:
    2nh6RzK.png

    2. Relevant equations
    E-L equation with dissipation: ##\frac{\partial\mathcal{L}}{\partial q_i} - \frac{d}{dt}\frac{\partial\mathcal{L}}{\partial\dot{q}_i} + \frac{\partial D}{\partial\dot{q}_j} = 0##

    3. The attempt at a solution
    I am going to use the generalized coordinate theta.

    For the circular mass, I have the potential energy to be ##mg(1-\cos(\theta)) = \frac{mg\theta^2}{2}## and the kinetic energy is ##\frac{1}{2}J\dot{\theta}^2## where J is the mass moment of inertia. The potential energy of the spring is ##\frac{1}{2}kx^2##, and the dissipative energy is ##D = c\frac{\dot{x}^2}{2}##.

    Before I convert the xs to thetas am I missing a kinetic or potential energy?
     
  2. jcsd
  3. Oct 1, 2014 #2

    BvU

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    Don't think you are missing anything. I do worry about the potential energy signs.
     
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