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7.8: Generalized energy theorem
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/07%3A_Symmetries_Invariance_and_the_Hamiltonian/7.08%3A_Generalized_energy_theorem
The Hamiltonian and generalized energy are constants of motion if the Lagrangian is a constant of motion and the external nonpotential forces are zero.
8.3: Hamilton’s Equations of Motion
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/08%3A_Hamiltonian_Mechanics/8.03%3A_Hamiltons_Equations_of_Motion
Canonical equations of motion.

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