2025 (Current Year) Faculty Courses School of Science Undergraduate major in Physics
Analytical Mechanics (Exercise) B
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Kazuki Yamamoto / Kazuya Fujimoto / Teruaki Suyama
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon
- Class
- B
- Course Code
- PHY.Q216
- Number of credits
- 010
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Apr 2, 2025
- Language
- Japanese
Syllabus
Course overview and goals
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.
Course description and aims
- 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.
Keywords
Lagrangian, Hamiltonian, symmetry
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Basic concepts and formulations are explained in lecture classes and concrete problems are given and then solved by students in exercise classes.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None.
Reference books, course materials, etc.
Problem sets will be distributed.
Evaluation methods and criteria
Based on blackboard presentation, report and examination.
Related courses
- PHY.Q206 ： Analytical Mechanics(Lecture)
- ZUB.Q204 ： Quantum Mechanics I
Prerequisites
Concurrent registration for the lecture class is highly recommended.