Canonical Transformations in Hamiltonian Mechanics

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Canonical Transformations: Phase Portraits and Action Variables

Explores canonical transformations, phase portraits, and action variables in Hamiltonian systems and harmonic oscillators.

Hamilton-Jacobi Equations: Phase Portrait

Explores Hamilton-Jacobi equations, phase portrait, and period calculation using action-angle variables for system trajectories.

Canonical Transformations in Hamiltonian Formalism

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

Canonical Transformations in Analytical Mechanics

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

Analytical Mechanics: Lagrange Formalism

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

Conservation Laws: General Framework

Covers the fundamental conservation laws and properties of space and time beyond mechanics.

Hamiltonian Mechanics: Analytical Approach

Explores Hamiltonian mechanics, conservation laws, potential functions, and canonical transformations in analytical detail.

Canonical Transformations: Hamilton-Jacobi Equation

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

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: Existence and Equations

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