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This lecture covers the application of Hamiltonian mechanics in polar coordinates, focusing on diatomic molecules after removing the center-of-mass motion. It discusses the Lagrange equations, conservation of energy, and the Hamiltonian for diatomic molecules. The instructor explains the concepts of canonical momentum, angular momentum, and the centrifugal force. The lecture also delves into the derivation of equations of motion from the principle of least action and the vibrational and rotational motion of molecules.