Field Theory: Action Principles

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Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

Introduction to Field Theory

Introduces field theory, focusing on density, springs, canonical transformations, and the principle of least action.

Principle of Least Action

Explores the principle of least action in mathematics and its application to functional branches.

Canonical Transformations in Hamiltonian Formalism

Explores canonical transformations in Hamiltonian formalism, emphasizing preservation of the action principle and structure necessary for transformations.

Variational Methods: Shortest Time Path Problem

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

Hamiltonian Formulation and Equivalence with Euler-Lagrange

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

Hamiltonian Mechanics: Phase Space and Poisson Bracket

Explores phase space, the Poisson bracket, and Hamiltonian mechanics concepts.

Principle of Least Action

Covers the principle of least action in mechanics and stress forces application.

Classical Mechanics: Newton, Lagrange, Hamilton

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

Analytical Mechanics: Equilibrium Positions and Least Action Principle

Explores equilibrium positions, lineic density, and the principle of least action in analytical mechanics.