Physics, Lagrangian, Symmetry, Classical Mechanics, Mechanics.
a single sum: (22) (23) To introduce a time derivative term, we use the Euler-Lagrange equations to substitute the partial derivative terms: (24) (25) The partial derivatives inside the sum are just the linear momenta pᵢ’ of the N particles of the system. Taking ϵₖ to zero, the prime symbols are