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Degrees of Freedom for a Lagrangian System

  1. Mar 5, 2015 #1
    1. The problem statement, all variables and given/known data

    A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance l from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force of strength k. The system is subject to gravity g. The constant k is given by k = mg/2l.

    State the degrees of freedom and choose appropriate coordinates

    2. Relevant equations


    3. The attempt at a solution

    I believe the degree of freedom is 2 with coordinates being θ: the angle of the rod and the distance of the second particle from the origin O. Although I am stuck on which coordinate I should use for that distance

  2. jcsd
  3. Mar 5, 2015 #2
    You are correct about the number of degrees of freedom. It shouldn't really matter what you call the position of the second mass along the rod, as long as you identify what you mean. Just pick a variable name such as ##a## or ##r_2## and write a description next to it telling what it means or draw it on a diagram.
  4. Mar 5, 2015 #3
    So would it be correct to use polar coordinates then?

    So then r would be the distance for the 2nd particle and it is related to the kinetic energy by x=rcosθ y=rsinθ and the first particle has fixed r=l?

    Thanks for your swift response!
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