1. Not finding help here? Sign up for a free 30min 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!

Action under a boost

  1. Jun 12, 2015 #1
    1. The problem statement, all variables and given/known data

    Calculate the variation of the action ##S = \int L dt = \int \frac{1}{2} m v^{2} dt## under a boost ##\vec v \rightarrow \vec v + \vec v_{0}##.

    2. Relevant equations

    3. The attempt at a solution

    ##\delta S##
    ##= \int \delta L\ dt##
    ##= \int \frac{1}{2} m\ \delta(\vec v^{2})\ dt##
    ##= \int \frac{1}{2} m\ \delta(v^{2} + vv_{0}cos \theta + v_{0}^{2})\ dt##
    ##= \int \frac{1}{2} m\ (2 v\ \delta v + v_{0}\ cos \theta\ \delta v )\ dt##
    ##= \bigg( \int (mv + v_{0} cos \theta)\ dt\ \bigg)\ \delta v##

    Am I correct so far?
     
  2. jcsd
  3. Jun 13, 2015 #2
    ## \delta{v^2} = 2\mathbf{v}\cdot\delta{\mathbf{v}} ##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Action under a boost
Loading...