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Problem with Lagrange first kind equations

  1. Jan 29, 2014 #1
    1. The problem statement, all variables and given/known data
    Two masses move in a plane restricted to concentric circles with radii R1 and R2. They are joined by a solid rod of length B. Use Lagrange first order equations to find the equilibrium point


    2. Relevant equations
    Constraint due to the solid bar: B = R12 + R22 -2R1R2cos(θ1 + θ2), where θ1 and θ2 are the polar coordinates of the masses.

    3. The attempt at a solution
    My Langrangian is as follows: L = (m/2)(R12ω12+R22ω22)-mg(sinθ1+sinθ2)
    By substituing in this expression http://en.wikipedia.org/wiki/Lagrangian_mechanics#Lagrange_equations_of_the_first_kind I find two equations of motion:
    -mgcos(θ1)+mR12+α1 + R1R2sin(θ1 - θ2)λ1 = 0
    -mgcos(θ2)+mR22+α2 - R1R2sin(θ1 - θ2)λ2 = 0
    where α1 and α2 are the angular accelerations of the masses, and the λs are the Lagrange multipliers. I can't solve this equations, though. Is there any method of solving them that I cannot find or is it that my whole procedure is wrong?
     
    Last edited: Jan 29, 2014
  2. jcsd
  3. Jan 29, 2014 #2

    CompuChip

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    Can you show us what your Lagrangian looks like, that you use to derive these equations of motion?
    You denoted the constraint by ##L##, but I don't think that expression is your Lagrangian because I don't see a kinetic term.
     
  4. Jan 29, 2014 #3
    Sorry, its a bit confusing because the length of the bar is L. I'll change it to B and edit the rest.
     
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