1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook