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- Academic unit or major
- Physics
- Instructor(s)
- Yamaguchi Masahide Watabiki Yoshiyuki
- Class Format
- Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-6(H102,H104)
- Group
- -
- Course number
- ZUB.Q212
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 2Q
- Syllabus updated
- 2019/4/5
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
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.
Student learning outcomes
- 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 that will be developed
| ✔ 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/Required learning
| 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 |
Textbook(s)
None.
Reference books, course materials, etc.
Problem sets will be distributed.
Assessment criteria and methods
Evaluated based on presentation, mini-exams, and term papers.
Related courses
- ZUB.Q203 ： Classical Mechanics
- ZUB.Q204 ： Quantum Mechanics I
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Concurrent registration for the lecture class is highly recommended.
