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Lagrangian problem setup question.

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider a particle of mass m moving in a vertical x-y plane along a curve y = a*cos((2[itex]\pi[/itex]x)/[itex]\lambda[/itex]). Consider its motion in terms of two coordinates x and y.
    Find Lagrange's equations of motion with undetermined multipliers.

    2. Relevant equations
    y = a*cos((2[itex]\pi[/itex]x)/[itex]\lambda[/itex]);
    (partial L/partial x) - d/dt(partial L/partial x dot) + [itex]\lambda[/itex]*(partial L/partial x) (sorry, couldn't figure out how to write the formula)

    3. The attempt at a solution
    All problems that we have been given of this type have had two independent equations for x and y. In this one y depends on x. I attempted to use the parameters x=x and [itex]\dot{x}[/itex]=[itex]\dot{x}[/itex]. The calculations are too long to post, but the answer I am getting for x double dot is crazy. I can see from the picture that y=a at x=0 and at x=[itex]\lambda[/itex]. Is there a way to use that to get my independent x parameter? If this problem belongs in the advanced physics forum, please let me know. Thank you in advance.
     

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    Last edited: Mar 24, 2012
  2. jcsd
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