Lectures related to Constraints and Lagrange

Molecular dynamics under constraints

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

Analytical Mechanics: Lagrange Formalism

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

Constraints and Lagrange

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

Mechanics: Geometric Constraints and Equilibrium Points

Explores generalized coordinates, constraints, equilibrium points, and stability in mechanics using elegant polar coordinates.

Simple Pendulum: Constraints and Equations of Motion

Explores the analysis of a simple pendulum, discussing constraints, forces, and equilibrium points.

Mechanics: Equilibrium Points and Stability

Explores equilibrium points and stability in mechanical systems, analyzing how systems return to or move away from their positions after disturbances.

Generalized Coordinates: Constraints, Equilibria, Stability

Covers generalized coordinates, constraints, degrees of freedom, and equilibrium points in mechanics.

General Physics: Mechanics for SIE and GC

Covers constraints, equilibrium points, and stability in mechanics using examples like pendulums.

Optimization: Constrained Volume Problems

Explores constrained volume problems using Lagrange multipliers to find extrema under constraints in various examples.

Principle of Least Action

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

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Conservation of Momentum and Kinetic Energy

Explores conservation of momentum and kinetic energy in collisions, emphasizing the importance of understanding collision outcomes.

Optimization with Constraints: KKT Conditions

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.

Particle Interactions: Forces and Newton's Laws

Explores particle interactions, forces, Newton's laws, and the center of mass in systems.

Newton's Laws of Motion

Covers Newton's Laws of Motion, action-reaction, conservation of momentum, and fundamental interactions in physics.

Quantité de mouvement and Impulsion

Explores momentum, impulse, work, energy, and angular momentum in advanced physics.

Conservation of Energy: Work and Potential Energy

Explores conservative forces, work, and potential energy calculations.

Newton's Laws: Inertia and Motion

Covers Newton's first and second laws, inertia, force, momentum, and action-reaction principle in mechanics.

Newton's Laws: Advanced Physics

Explores Newton's laws of motion, covering inertia, force, acceleration, action, reaction, frames of reference, and measurement of force.

Constraints in Molecular Dynamics: Theory and SHAKE Algorithm

Explores the theory of constraints in molecular dynamics simulations, including the SHAKE algorithm.