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Homework Help: Lagrange multipliers rotating masses connected by spring

  1. Sep 12, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle of mass, m1, is constrained to move in a circle with radius a at z=0 and another particle of mass, m2, moves in a circle of radius b at z=c. For this we wish to write up the Lagrangian introucing the constraints by lagrange multipliers and solve the following equations of motion.

    2. Relevant equations

    Equations of constraint.

    [tex]z1=0\ \ x1^2+y1^2=a^2[/tex]
    [tex]z2=c \ \ x2^2+y2^2=b^2[/tex]

    3. The attempt at a solution

    I am working on the Lagrangian given by



    From this we get the equations of motion:






    [tex]m_2\ddot{z_2}=k\left(z_2-z_1\right)-\lambda_2 [\tex]

    Anyone know how to solve these equations of motion
  2. jcsd
  3. Sep 14, 2008 #2
    You could reduce the number of coordinates by introducing polar coordinates for each mass. There would be less equations to solve.
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