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For a given dynamical system with N degrees of freedom q = (q1,…,q N ) characterized by the Hamiltonian function H = ∑ k = 1 N q ˙ k ∂ L / ∂ q ˙ k − L Open image in new window, it is effortless to check that the Hamiltonian is not a constant of motion, i.e., the conservation of energy is violated.
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