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Lecture# Hamiltonian Mechanics: Diatomic Molecules

Description

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.

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In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.

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In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.

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