Concept

Euler–Lagrange equation

Related lectures (32)

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

Covers the Euler-Lagrange equation in Sobolev spaces and discusses minimization, convexity, and weak forms.

Covers the Lagrange method for expressing constraints and degrees of freedom in mechanics using generalized coordinates.

Principle of Least Action

Covers the principle of least action, Euler-Lagrange equations, Lagrange multipliers, and variational calculus.

Molecular dynamics under constraints

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

Coupled Pendulums: Lagrange Mechanics

Covers the Lagrange mechanics of coupled pendulums and their equations of motion.

Tensioner of a Rotating Drum: Vibratory Mechanics

Analyzes a tensioner system for a rotating drum using Lagrange equations.

Hamiltonian Formulation and Equivalence with Euler-Lagrange

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

Dynamics of Mechanical Systems

Explores the laws of space, kinematics, and inertia forces in mechanical systems.

Dynamics of Mechanical Systems: Kinematic Laws and Equations of Motion

Explores kinematic laws, forces-motion coupling, Lagrange formulation, and equations of motion in mechanical systems.

System Dynamics: Trajectory Analysis

Covers the analysis of trajectories in system dynamics and solutions to the dynamics.

Generalized Oscillator: Vibratory Mechanics

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

Stellar Orbits: Lagrange Points

Explores stellar orbits in rotating potentials, focusing on surfaces of section, integrals of motion, and stability around Lagrange points.

Classical Mechanics: Newton, Lagrange, Hamilton

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

Lagrange II: Compound Pendulum Analysis

Explores the dynamics of a compound pendulum, emphasizing inertia and energy analysis.

Lagrange's Method in Mechanics

Covers Lagrange's method in mechanics, focusing on handling constraints and deriving equations of motion.

Calculus of Variations: Some Topics

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

Experiments, Holonomic Constraints

Covers time-independent and time-dependent constraints in mechanics, balance, small oscillations, Lagrange method, kinetic energy, equilibrium, and stability.

Field Theory: Action Principles

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

Lagrangian Mechanics

Covers Lagrangian mechanics, a method simplifying equations of motion by focusing on energy concepts and generalized forces in complex systems.