Relativistic Lagrangian, Principle of Least Action And Hamiltonian | Relativistic Mechanics

[@joeboxter3635]

As v -> c, gamma tends towards 0. Thus the reciprocal tends to infinity. Thus if we say dtau = 1/gamma * dt, then for a small passage of time, your proper time would be much larger as v -> c. But that is not the typical definition of "proper time". Proper time is the time as measured by the moving body not an external reference. And proper time should dtau -> 0 as v -> c. But you have it backwards. Also, I think you need to use two different words "coordinate time" and "proper time" where "coordinate time" is the rest reference frame and "proper time" is the time inside the body that is moving.

[@2tehnik]

Did you need to go through the derivation of the euler-lagrange equation? Isn’t it the same as in classical mechanics? Also, how is the Lagrangian Lorenz invariant? Given that it has the Lorenz factor.