Analytical mechanics is the mathematically sophisticated reformulation of Newtonian mechanics and consists of Lagrangian mechanics and Hamiltonian mechanics. Not only does analytical mechanics enable us to solve problems efficiently, but it also opens up a route leading to quantum mechanics.
The objective of this course is to learn the following subjects in Lagrangian mechanics and Hamiltonian mechanics.
- Being able to express and solve problems of mechanics with the use of Lagrangian and Hamiltonian.
- Being able to explain roles of symmetry in physics.
Lagrangian, Hamiltonian, symmetry
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Basic concepts and formulations are explained in lecture classes and concrete problems are given and then solved by students in exercise classes.
|Course schedule||Required learning|
|Class 1||Equations of Motion and Coordinate Systems||Understand contents and results in each class and should be able to derive and explain them by oneself. Also, be able to solve related concrete problems.|
|Class 2||Euler-Lagrange Equation|
|Class 3||Generalized Coordinates and Covariance|
|Class 4||Principle of Least Action|
|Class 5||Construction of Lagrangians|
|Class 6||Symmetries and Conversation Laws|
|Class 7||Treatment of Constraints|
|Class 8||Small Oscillations|
|Class 9||Phase Space and Canonical Equations|
|Class 10||Canonical Transformations|
|Class 11||Liouville's Theorem|
|Class 12||Infinitesimal Transformations and Conserved Quantities|
|Class 13||Poisson Bracket|
|Class 14||Hamilton-Jacobi Equation|
|Class 15||Periodic Motion and Canonical Variables|
Lecture notes will be distributed via OCW-i.
Problem sets will be distributed.
Evaluated based on presentation, mini-exams, and reports in exercise classes (~40%) and final examination (~60%).