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
|✔ Specialist skills||Intercultural skills||Communication 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 / Euler-Lagrange Equation||Be able to solve concrete problems related to contents in each class.|
|Class 2||Generalized Coordinates and Covariance / Principle of Least Action|
|Class 3||Construction of Lagrangians / Symmetries and Conversation Laws|
|Class 4||Treatment of Constraints / Small Oscillations|
|Class 5||Phase Space and Canonical Equations / Canonical Transformations|
|Class 6||Liouville's Theorem / Infinitesimal Transformations and Conserved Quantities|
|Class 7||Poisson Bracket / Hamilton-Jacobi Equation|
|Class 8||Periodic Motion and Canonical Variables|
Problem sets will be distributed.
Evaluated based on presentation, mini-exams, and term papers.
Concurrent registration for the lecture class is highly recommended.