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Homework Help: Double Pendulum Lagrange's Equation Problem

  1. Nov 6, 2008 #1
    1. The problem statement, all variables and given/known data
    A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lengths and have bobs of equal mass and if both pendula are confined to move in the same plane, find Lagrange's equations of motion for the system. Do no assume small angles.

    2. Relevant equations
    partial L/partial q-(d/dt)(partial L/partial q')+lambda(partial f/partial q)

    3. The attempt at a solution
    Main problem is finding an equation of constraint to use. I know the motion of the pendula must be dependant on each other since they are connected, but not sure how to correctly state that. Also, do I need to set things up piece by piece? Meaning, have an equation of motion for x1,x2,y1,and y2? Or should it be combined?
  2. jcsd
  3. Nov 7, 2008 #2


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    Homework Helper
    Gold Member

    Well, suppose that the upper pendulum hangs from the origin, and its bob has coordinates [itex](x_1(t),y_1(t))[/itex] at time [itex]t[/itex]....can you find an expression for the length of that pendulum as a function of [itex]x_1(t)[/itex] and [itex]y_1(t)[/itex]?

    How about the length of the second pendulum if its bob has coordinates [itex](x_2(t),y_2(t))[/itex] at time [itex]t[/itex]? (keep in mind that the second pendulum is not hanging from the origin :wink:)

    That should give you two constraint equations.
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