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I've heard it said that the Lagrangian of a free particle cannot possibly be a function of any position coordinate, or individual velocity component, but it is a function of the total magnitude of velocity. Why is this the case? I'd be grateful for any pointers in the direction of either a physical or a mathematical explanation
EDIT: I should make it clearer that this is assuming no prior knowledge of kinetic energy or Newton's laws
EDIT: I should make it clearer that this is assuming no prior knowledge of kinetic energy or Newton's laws
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