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!

Lagrangian for free particle

  1. Jun 11, 2008 #1
    In section 4 of Landau and Lifgarbagez they derive the expression for the kinetic energy by expanding the Lagrangian around v+e. The resulting expression has a term which must be a total time derivative so that the equations of motion are unaffected. The text claims that the term dL/d(v^2) v.e must be linear in v to be a total time derivative, but I don't understand why this is.
  2. jcsd
  3. Jun 17, 2008 #2
    I just read that section.
    I think it would have helped if they stated that the 2nd term is a total time derivative 'of a function of coordinates and time' ...
    df(x,t) / dt = df/dx * dx/dt + df/dt (partial d's now)
    Since f does not depend on the velocities, df/dx and df/dt don't, and the overall dependence of df/dt on v=dx/dt is linear.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Lagrangian free particle Date
The Lagrangian of a free particle. (mv²/2) Jun 19, 2014
Lagrangian of a free particle Feb 23, 2012
Lagrangian for a free particle Nov 16, 2011
Lagrangian of a free particle Mar 2, 2010
The Lagrangian for a free particle Jul 28, 2009