Lectures in course PHYS-202: Analytical mechanics (for SPH)

Hamilton's Formalism: Equations and Transformations

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

Explores symmetry in Lagrangian mechanics and its impact on physical systems.

Analytical Mechanics: Newton's Three Laws

Introduces the mathematical approach to analytical mechanics, emphasizing Newton's three laws for a complete description of phenomena.

Quantum Mechanics: Jacobi Identity and Gauge Invariance

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

Constraints and Lagrange

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

Conservation of Energy in Mechanics

Explains how total mechanical energy remains constant over time despite forces, using mathematical equations and examples.

Hamilton Formalism: Normal Coordinates

Covers the Hamilton formalism applied to normal coordinates and constraints.

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.

Conservation of Energy in Mechanics

Covers the conservation of energy in mechanics through equations and examples.

Canonical Transformations: Rules and Equations

Explores canonical transformations, rules, equations, gauge invariance, and the principle of least action.

Constraints and Lagrange Formalism

Covers constraints in physics, degrees of freedom, and Lagrange formalism with a focus on mathematical representations.

Principle of Least Action

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

Canonical Transformations: Hamiltonian Equations

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

Lagrange's Approach: Dynamics and Constraints

Explores Lagrange's approach to dynamics, emphasizing compatibility with constraints and the significance of generalized coordinates.

Variational Calculus and Least Action Principle

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

Principle of Least Action

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

Canonical Transformations 2

Explores canonical transformations, symplectic matrices, and the concept of identity in matrix space.

Canonical Transformations: Hamilton-Jacobi Equation

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

Symmetry and Conservation Laws

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

Canonical Transforms: Hamilton-Jacobi Equation

Explores canonical transforms and the Hamilton-Jacobi equation, emphasizing explicit solutions and initial conditions.