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School of Engineering
- Undergraduate major in Mechanical Engineering
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- Common courses
- School of Materials and Chemical Technology
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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Earth and Planetary Sciences
- Instructor(s)
- Imaeda Yusuke
- Class Format
- Lecture / Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-6(I123) Fri3-6(I123)
- Group
- -
- Course number
- EPS.B203
- Credits
- 4
- Academic year
- 2020
- Offered quarter
- 2Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This lecture presents the basics of analytical mechanics, such as generalized coordinates,Euler-Lagrange equation, variation principle, Hamiltonian formalism, and canonical transformation.
As actual applications of analytical mechanics, physical phenomena like Kepler motion, coupled oscillation, motion in rotating frame, rigid-body motion are focused.
This lecture also involves abundantexercise to master the application of analytical mechanics to actual physical phenomena.
Half of the time is spent for lecture and the other half is spent for exercise every week.
Student learning outcomes
This lecture aims at understanding the concept and method of analytical mechanics, on which many parts of modern physics are now based. It also aims at getting used to practical applications of analytical mechanics through intensive exercise.
Keywords
Lagrange formalism, variation principle, Hamiltonian formalism, Canonical Transformation
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
This course consists of concurrent lectures and exercises.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Preparation for Analytical Mechanics | Coordinates, Derivative |
| Class 2 | Introduction to Lagrange Formalism I | Lagrangian, Generalized coordinate |
| Class 3 | Introduction to Lagrange Formalism II | Application of Lagrange equation |
| Class 4 | Conservation Laws in Analytical Mechanics | Conservation of energy, momenta, and angular momenta |
| Class 5 | Motion in a central force field | Kepler motion |
| Class 6 | Micro Vibration | One-dimensional and multi-dimensional vibrations |
| Class 7 | Normal Vibration | Eigenfrequency |
| Class 8 | Motion in a Rotating Frame | Force of inertia |
| Class 9 | Rigid-body Motion | Rotational energy, Moment of inertial |
| Class 10 | Variation Principle | Functional, Euler equation |
| Class 11 | Hamilton Formalism and Canonical Equation | Legendre transformation, Hamiltonian |
| Class 12 | Canonical Transformation | Hamilton-Jacobi equation |
| Class 13 | Exercise of Analytical Mechanics | Solve problems using Lagrange and Hamiltonian formalism |
| Class 14 | Examination | Examination |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
■ Landau-Lifshitz, "Mechanics, Third Edition: Volume 1" (Course of Theoretical Physics), Butterworth-Heinemann (English or Japanese)
■ Yasushi Suto, "Analytical Mechanics and Quantum Mechanics", University of Tokyo Press (Japanese)
■ Shoichiro Koide, Introduction Course in Physics Vol.2“Analytical Mechanics”, Iwanami Shoten Publishers, ISBN4-00-007642-6 (Japanese)
■ Isao Imai, "Exercise in Mechanics", Science Press (Japanese)
■ Ryuzo Abe, Textbook in Physics Vol.6 "Introduction in Quantum Mechanics", Iwanami Shoten Publishers, ISBN4-00-007746-5 (Japanese)
Assessment criteria and methods
Student performance will be assessed by the combination of the exercise (40%), and the final exam in the 15th lecture (60%).
Related courses
- PHY.Q206 ： Analytical Mechanics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None
