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.
|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|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content.
They should do so by referring to textbooks and other course material.
Concurrent registration for the exercise class is highly recommended.