In the lagrangian solution for the equation of motion, there's a seemingly out of place ddt∂V∂˙qj
term. Potential energy is usually a function of the set of xi or position only. If xi can all be rewritten as functions of only qi and t, and qi can be varied without having to change ˙qi. Then we're left with this term being precisely 0
So at least for conservative forces, this term should equal zero. But where do we find cases where it isn't? Magnetic forces? Is it frictional forces (what is potential for a frictional force anyway? And does Lagrange's equation even work for inelastic systems, considering energy is not conserved?)
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