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Lagrange Function for a certain problem

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is connected by a massless spring of force constant k and unstressed
    length r0 to a point P that is moving along a horizontal circular path of radius a at a
    uniform angular velocity ω. Verify the Lagrange-Function!

    2. Relevant equations

    Could there be a typing error in the book (the book provided the solution which can be seen in the file "function.png". My own solution just differs in the term with r and has 1/2*m*r^2*theta' instead of 1/2*m*r*theta' like shown in the book. However i think my solution is right or can anybody find a mistake?

    3. The attempt at a solution

    x[1](t):=a*cos(omega*t)#`this is the x-coordinate of P
    y[1](t):=a*sin(omega*t)#`this is the y-coordinate of P
    x[2](t):=x[1](t)+r(t)*cos(theta(t))#`this is the x-coordinate of m
    y[2](t):=y[1](t)+r(t)*sin(theta(t))#`this is the y-coordinate of m
    T := (1/2)*m*((diff(x[2](t), t))^2+(diff(y[2](t), t))^2)
    V :=(1/2)*k*(r-r[0])^2
    L=T-V

    I attached a drawing of the exercise and two lagrange functions (from the book and my solution) and a Maple file for convenience.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 17, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Your answer is almost certainly correct. That term in the books answer doesn't have consistent dimensions with the terms around it.
     
  4. Dec 17, 2011 #3
    Ah yeah. I should have checked the dimensions as well! Thanks for the advice!
     
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