Is the Particle Free? Calculating Equations of Motion

[freesnow]

Homework Statement

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

Homework Equations

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...

 

[gabbagabbahey]

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.[/tex]