Hamilton-Jacobi Equation: Analytical Mechanics

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Explores canonical transformations in Hamiltonian mechanics, emphasizing variable separation in the Hamilton-Jacobi equation.

Introduces the basics of finite element modeling for dynamics and discusses the Newmark method for time integration.

Covers the fundamental concepts of mechanics, focusing on forces and motion.

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Explores the harmonic oscillator, covering energy functions, equations of motion, and operator constructions.

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Covers the mechanics of springs, analyzing forces and elongations in connected springs.

Explores Hamilton-Jacobi equations, phase portrait, and period calculation using action-angle variables for system trajectories.

Covers geometric locus, cone sections, Kepler's problem, Newton's laws, and conservation laws.

Explores the Ehrenfest Theorem, connecting quantum and classical mechanics through expectation values and harmonic oscillator dynamics.