Lectures related to Analytical Mechanics: Equilibrium Positions and Least Action Principle

Covers the principle of least action in mechanics and stress forces application.

Analytical Mechanics: Principle of Least Action

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

Explores quantum instanton theory, path integrals, reaction rates, and tunnelling phenomena.

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

Hamilton's Formalism: Equations and Transformations

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

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.

Derivation of Boundary Conditions in Mechanics of Slender Structures

Covers the derivation of boundary conditions in mechanics of slender structures, focusing on total energy variation and equilibrium equations.

Introduction to Field Theory

Introduces field theory, focusing on density, springs, canonical transformations, and the principle of least action.

Quantum Chemistry: Postulates and Harmonic Oscillator

Explores the historical perspective and postulates of quantum mechanics, focusing on the harmonic oscillator and approximation methods.

Symmetry and Conservation Laws

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

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Geodesics and Surface Area

Explores geodesics as locally shortest paths and defines surface area using parametric squares.

Variational Calculus and Least Action Principle

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

Principle of Least Action

Explores the principle of least action in mathematics and its application to functional branches.

Hamiltonian Mechanics: Phase Space and Poisson Bracket

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

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

Quantum Chemistry Fundamentals

Covers the basics of quantum chemistry and the Hartree-Fock method.

Quantum Mechanics: Path Integral Representation

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