Analytical Mechanics

Course Purpose
The purpose of this course is for students to learn the classical mechanics, i.e., Newtonian mechanics, through the Lagrange's formalism and the Hamilton's formalism, as well as the variational principle.
Learning Goals
The purpose of this course is for students to use Lagrange's equation of motion and Hamilton's canonical equations of motion to analyse various mechanical systems.
Topic
Session 1Coordinates and coordinate transformations
Session 2Equation of motion: Generalized coordinates and binding conditions
Session 3Derivation of Euler-Lagrange equation
Session 4Analysis of minute vibrations by Lagrange equation
Session 5Derivation of Euler equations by variational method
Session 6Hamilton's principle and Euler-Lagrange equation
Session 7Lagrange equation and circular coordinates, rotating coordinate system, time propulsion
Session 8Lagrange equation and symmetry
Session 9Noether's theorem, Lagrange's undetermined multiplier method
Session 10Canonical theory (1) Canonical equations and Hamiltonian
Session 11Canonical theory (2), Motion of charged particles in magnetic field and Lagrangian, Hamiltonian
Session 12Phase space, Poisson bracket
Session 13Canonical transformation 1
Session 14Canonical transformation 2
＊＊This content is based on April 1, 2024. For the latest syllabus information and details, please check the syllabus information inquiry page provided by the university.＊＊