Principle of Least Action

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Lagrangian Mechanics: Symmetries and Conservation Laws

Explores Lagrangian mechanics, symmetries, conservation laws, and the Hamiltonian concept.

Constraints and Lagrange

Covers constraints, Lagrange equations, generalized coordinates, cyclic coordinates, conservation laws, and Hamilton formalism.

Variational Calculus and Least Action Principle

Covers the principle of least action and variational calculus in discovering equations of motion.

Molecular dynamics under constraints

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

Analytical Mechanics: Principle of Least Action

Covers the principle of least action and constraint handling in analytical mechanics.

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Symmetries in Mechanics and Wave Equations

Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.

Calculus of Variations: Some Topics

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

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.

Analytical Mechanics: Lagrange Formalism

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.