Lectures related to Stellar Orbits and Potential Theory

Lagrangian Mechanics: Symmetries and Conservation Laws

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

Canonical Transformations in Analytical Mechanics

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

Quantum Harmonic Oscillator

Explores the classical dynamics and quantization of a harmonic LC oscillator.

Galaxy Disk Models: Orbits and Potentials

Explores galaxy disk models, orbits, potentials, and circular velocity in disk galaxies.

Thermodynamic Potentials: Lagrangian Mechanics and Energy Relations

Discusses the transition from Hamiltonian to Lagrangian mechanics, focusing on thermodynamic potentials and their implications in energy transformations.

Quantum Mechanics: Path Integral Representation

Covers the path integral representation in quantum mechanics and the dynamics of systems described by Lagrangian.

Constraints and Lagrange

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

Analytical Mechanics: Lagrange Formalism

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

Bulky Hamiltonian isotopies

Explores the concept of bulky Hamiltonian isotopies of Lagrangian tori.

Hamiltonian Mechanics: Diatomic Molecules

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

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.

Classical Mechanics: Newton, Lagrange, Hamilton

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

Symmetry and Conservation Laws

Explores symmetry, Noether's theorem, and conservation laws in physics, emphasizing the role of time and the Hamiltonian.

Non-linear dynamics: phenomenology, tools and methods

Explores Hamiltonian and Lagrangian formulations, canonical variables, Lie operators, and their applications in beam dynamics and nonlinear systems.

Canonical Transformations: Hamiltonian Equations

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

Hamiltonian Mechanics: Phase Space and Poisson Bracket

Explores phase space, the Poisson bracket, and Hamiltonian mechanics concepts.

Field Theory: Action Principles

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

Harmonic Oscillator

Explores the harmonic oscillator, covering energy functions, equations of motion, and operator constructions.

Molecular dynamics: Integrating Newton's equations

Explores molecular dynamics, integrating Newton's equations to make atoms move according to interatomic forces.

Harmonic Oscillator: Algebraic Approach

Explores the classical harmonic oscillator and its algebraic approach to studying the system.