Lagrange's Method in Mechanics

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Hamiltonian Formulation and Equivalence with Euler-Lagrange

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.

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Explores equilibrium points and stability in mechanical systems, analyzing how systems return to or move away from their positions after disturbances.

Harmonic Oscillator: Algebraic Approach

Explores the classical harmonic oscillator and its algebraic approach to studying the system.

Classical Mechanics: Newton, Lagrange, Hamilton

Covers classical mechanics, including Newton's, Lagrange's, and Hamilton's formulations for calculating particle positions over time.

Mechanics: Geometric Constraints and Equilibrium Points

Explores generalized coordinates, constraints, equilibrium points, and stability in mechanics using elegant polar coordinates.

Harmonic Oscillator

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

Introduction to Mechanics: Historical Overview and Fundamentals

Provides an overview of the historical development and fundamental concepts in mechanics, emphasizing the interplay between potential and kinetic energy.

Work and Energy: Mechanics

Explores work in mechanics, kinetic and potential energy, conservative forces, and the conservation of mechanical energy.

Conservation of Energy in Mechanics

Explains how total mechanical energy remains constant over time despite forces, using mathematical equations and examples.

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Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.