- #1
spaghetti3451
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Homework Statement
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}##.
Homework Equations
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?