Analytical Mechanics

Course Purpose
To understand the equations of motion based on Hamilton's principle and be able to formulate the equations of motion in both Lagrangian and Hamiltonian form for a given system.
Learning Goals
To learn the fundamentals of the variational method, derive equations of motion using the Lagrangian and Hamiltonian, and apply them to the analysis of physical systems.
Topic
Session 1Newtonian mechanics review
Session 2Functionals and the calculus of variations, derivation of the Euler equations
Session 3Application of Euler's equation (Brachystochrone problem)
Session 4Lagrangian formalism and the principle of least action
Session 5Applications of the Euler-Lagrange equations
Session 6Lagrange's method of undetermined multipliers and its application to the physics of holonomic constrained systems (Double pendulum example)
Session 7Coupled oscillation
Session 8Legendre transform and Hamiltonian form (Canonical form)
Session 9Topological spaces and Poisson brackets
Session 10Canonical transformation
Session 11Hamilton-Jacobi equation
Session 12Coordinate transformation and conservation laws (Noether's theorem)
Session 13Introduction to analytical field mechanics
Session 14Derivation of Maxwell's equations
＊＊This content is based on April 1, 2025. For the latest syllabus information and details, please check the syllabus information inquiry page provided by the university.＊＊