Lectures related to Analytical Mechanics: Lagrange Formalism

Molecular dynamics under constraints

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

Constraints and Lagrange

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

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Canonical Transformations in Analytical Mechanics

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

Constraints and Lagrange

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

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

Hamiltonian Formalism: Conservation Laws

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Hamiltonian Mechanics: Diatomic Molecules

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

Canonical Transformations in Hamiltonian Formalism

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

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Hamilton's Formalism: Equations and Transformations

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

Principle of Least Action

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

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Classical Mechanics: Newton, Lagrange, Hamilton

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

Canonical Transformations: Hamiltonian Equations

Explores canonical transformations, emphasizing Hamiltonian equations, constant quantities, and the importance of Lagrangian variables.

Lagrangian Mechanics: Symmetries and Conservation Laws

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

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.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Mechanics: Geometric Constraints and Equilibrium Points

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