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Minkowski Force due to a quadratic in velocity potential

  1. Nov 13, 2016 #1
    1. The problem statement, all variables and given/known data
    A generalized potential suitable for use in a covariant Lagrangian for a single particle. This is Goldstein problem 9 chapter 7.

    −Aλν(xμ)uλuν

    where Aλν stands for a symmetric world tensor of the second rank and u^v are the components of the world velocity. If the Lagrangian is made up of (1/2)m*u_v*u^v minus U, obtain the Lagrange equations of motion. What is the Minkowski force? Give the components of the force as observed in some Lorentz frame.





    2. Relevant equations

    Euler equation of motion where the derivatives are taken with respect to the four velocity and where and the time part if the proper time. Also that the four force is the mass times the four velocity.

    3. The attempt at a solution

    When I workout the Lagrangian I have an extra term which is proportional to the four acceleration. My first thought is to solve for the four acceleration and then multiply it by the mass to get the Minkowski force. Is that valid?
     
  2. jcsd
  3. Nov 19, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Jun 10, 2017 #3
    Minkowski 4-Force = dP/d-tau where P is 4-momentum;
    or 4-Force = gamma(3-Force, id/dt(mc)) where m is relativistic mass.
     
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