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To show a particle is free

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    The one-dimensional motion of a particle with coordinate q is governed by the Lagrangian

    L = (dq/dt)2(6q2 - 4qt(dq/dt) + (dq/dt)2t2)

    Show that the particle must be free

    2. Relevant equations



    3. The attempt at a solution

    I know that L needs to depend only on (dq/dt)2 for the particle to be free, but I don't know how to do it...
     
  2. jcsd
  3. Oct 19, 2009 #2

    gabbagabbahey

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    One way to show that it is a free particle (i.e., there are no forces on it) is to calculate the equations of motion....if [tex]\ddot{q}=0[/itex], then Newton's second law tells you the net force on the particle is everywhere zero.
     
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