Physics, Lagrangian, Symmetry, Classical Mechanics, Mechanics.
derivative of L’: (19) (j is summed from 1 to n; i is summed from 1 to N) I’ve neglected the other two variables that the Lagrangian depends on since t’ = t and dx’/dt’ = dx/dt. However, notice how we can simplify the dx/dϵ term by realizing that if j = k, then the derivative is simply one,