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Lagrangian of system

  1. Dec 10, 2007 #1
    1. The problem statement, all variables and given/known data
    two masses, m1 and m2, are hung from a point, P, by two string, L1 and L2, the masses are connected by a rod, length D, of negligible mass. The angle between the strings is theta, the angle between L2 and horizontal line through P is Phi. so essentially it looks like a hanger with a mass at both ends of it.

    2. Relevant equations
    The formula for the Lagrangian is simply L=T-U, where T and U are the Potential and Kinetic energy.
    To find the energy I'm going to need velocity's which I think I can get by taking the Derivative of the position equations.

    3. The attempt at a solution
    I am going to use phi as my generalized coordinate, and if this were a simple pendulum I think this problem would be pretty easy, you take the derivative of your position equations to get velocity then use T=1/2MV^2 and U=mgh and then plug and chug. With this problem having two masses separated by a rigid rod I'm completely stumped on how to go about this. Any help at all is greatly appreciated.
  2. jcsd
  3. Dec 11, 2007 #2

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    In the triangle, theta will remain constant. Draw the diagram. L1 and L2 are the lengths of the strings.

    T = ½ I1w1^2 + ½ I2w2^2 = ½ m1*L1^2(dphi/dt) + ½ m2*L2^2(dphi/dt), since theta is a const.

    V = -m1h1 – m2h2 = -mL1sin phi – mL2 sin (phi + theta).

    Now you can set up L as phi as the only generalized co-ordinate.
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