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Concept

Lagrangian mechanics

Related lectures (31)

Constraints and Lagrange

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

Principle of Least Action

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

Generalized Forces: Modeling and Examples

Covers modeling systems with Lagrange formalism and examples of generalized forces in aerodynamics and drone propellers.

Optimal Control: Convergence and Conditions

Covers the convergence and conditions for optimal control.

Molecular dynamics under constraints

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

Lagrangian Mechanics: Symmetries and Conservation Laws

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

Variational Calculus and Least Action Principle

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

Bulky Hamiltonian isotopies

Explores the concept of bulky Hamiltonian isotopies of Lagrangian tori.

Coupled Pendulums: Lagrange Mechanics MOOC: Lagrangian Mechanics

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

Lagrange Method MOOC: Lagrangian Mechanics

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

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.

Hamilton's Formalism: Equations and Transformations

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

Classical Mechanics: Newton, Lagrange, Hamilton

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

Lagrange I: Conservation Laws and Kinetic Energy

Explores Lagrangian mechanics, conservation laws, and kinetic energy in generalized coordinates.

Lagrangian Mechanics

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

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Constraints and Lagrange

Introduces constraints, Lagrange multipliers, and generalized coordinates in physics.

Analytical Mechanics: Lagrange Formalism

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

Fluid Kinematics: Velocity Fields and Flow Visualization

Explores velocity fields and flow visualization in fluid kinematics, emphasizing streamlines, path lines, and streak lines.

Kinetic Energy of Rotating Discs and Bars

Covers kinetic energy, motion equations, and modeling of rotating discs and bars.