Lectures related to Constraints and Lagrange

Molecular dynamics under constraints

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

Principle of Least Action

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

Lagrangian Mechanics: Symmetries and Conservation Laws

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

Constraints and Lagrange

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

Mechanics: Geometric Constraints and Equilibrium Points

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

Analytical Mechanics: Lagrange Formalism

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

Hamiltonian Mechanics: Diatomic Molecules

Explores Hamiltonian mechanics in diatomic molecules, emphasizing polar coordinates and conservation laws.

Classical Mechanics: Newton, Lagrange, Hamilton

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

Lagrange Method

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

Molecular Dynamics Simulations: Basics and Algorithms

Covers the basics of molecular dynamics simulations, ensemble properties, classical mechanics formulations, numerical integration, energy conservation, and constraint algorithms.

Canonical Transformations in Analytical Mechanics

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

Symmetry & Boundary Conditions

Explores symmetry and boundary conditions in finite element models, emphasizing the importance of maintaining symmetry for accurate modeling.

Generalized Coordinates: Constraints, Equilibria, Stability

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

Hamiltonian Formulation and Equivalence with Euler-Lagrange

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

Analytical Mechanics: Principle of Least Action

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

Symmetries in Mechanics and Wave Equations

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

Hamilton's Formalism: Equations and Transformations

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

Symmetries of Newtonian Mechanics

Explores the symmetries of Newtonian Mechanics, Lagrangian mechanics, and the conservation of energy.

Center of Mass Calculation in Mechanics

Explores center of mass calculation in mechanics, emphasizing system symmetry and spherical coordinates for simplifying calculations.

Lagrange I: Conservation Laws and Kinetic Energy

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