Joseph-Louis Lagrange

Natural sciences
Physics
Mechanics
Classical mechanics

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Hamilton's Formalism: Equations and Transformations

Explores Hamilton's formalism, canonical equations, and Poisson brackets in classical and quantum mechanics.

Generalized Oscillator: Vibratory Mechanics

Explores the concept of a generalized oscillator in vibratory mechanics and its application to a two-degree-of-freedom system.

Stability of Lagrange Points

Explores the stability of Lagrange points in celestial mechanics, focusing on equilibrium in rotating frames and the dynamics of celestial bodies.

Molecular Dynamics Simulations: Basics and Algorithms

Covers the basics of molecular dynamics simulations, ensemble properties, classical mechanics formulations, numerical integration, energy conservation, and constraint algorithms.

Optimization with Lagrange Multipliers

Covers advanced optimization techniques using Lagrange multipliers to find extrema of functions subject to constraints.

Stationary Points and Lagrange Multiplier Theorem

Explores stationary points and the Lagrange multiplier theorem for function optimization.

Parametric Pendulum: Equations and Solutions

Analyzes a parametric pendulum using Lagrange method, Mathieu equation, and Ince method to find solutions.

Euler-Lagrange Equation: Convexity and Saddle Point Problems

Explores the Euler-Lagrange equation, convexity, and saddle point problems in variational calculus.

Calculus of Variations: Some Topics

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Field Theory: Action Principles

Discusses the application of action principles in classical field theory, focusing on Lagrange and Hamiltonian formulations.