授業の目的 【日本語】 Goals of the Course(JPN) | | |
|
授業の目的 【英語】 Goals of the Course | | This is the first of two courses in analytical mechanics. Analytical mechanics abstracts from Newtonian mechanics and generalizes it to a versatile framework that can be applied to various areas of physics, such as quantum mechanics, statistical mechanics, and relativity. After a survey of elementary principles, we discuss the core concepts of Lagrangian and Hamiltonian mechanics, with special emphasis on symmetry principles, followed by some explicit examples. |
|
|
到達目標 【日本語】 Objectives of the Course(JPN)) | | |
|
到達目標 【英語】 Objectives of the Course | | A student who successfully completes this course will be able to:
- Understand the notions and procedures of the calculus of variations
- Write down the Lagrangian of a mechanical system in terms of generalized coordinates and describe its motion using the Euler-Lagrange equations
- Understand the relation between symmetries and conservation laws and write down the associated conserved quantities
- Describe the motion of mechanical systems using Hamiltonians
- Describe motion in central force problem using effective potential |
|
|
授業の内容や構成 Course Content / Plan | | 1. Survey of elementary principles
2. Variational principles and Lagrangian mechanics
3. Symmetries and conservation laws
4. Hamiltonian mechanics
5. Central force problem |
|
|
履修条件 Course Prerequisites | | Calculus I & II, Fundamentals of Physics I &II, and concurrent registration of Mathematical Physics I & II |
|
|
関連する科目 Related Courses | | Analytical Mechanics II, Quantum Mechanics I |
|
|
成績評価の方法と基準 Course Evaluation Method and Criteria | | Attendance/Quizzes 10%, homework 30%, midterm 30%, final exam 30% |
|
|
不可(F)と欠席(W)の基準 Criteria for "Fail (F)" & "Absent (W)" grades | | The “Absent” grade is reserved for students who withdraw by the deadline. After that day, a letter grade will be given based on the assessment during the semester. |
|
|
参考書 Reference Book | | L. D. Landau and E. M. Lifschitz, "Mechanics: Volume 1 (Course of Theoretical Physics)", Butterworth-Heinemann; 3rd edition (1976), ISBN-10: 0750628960, ISBN-13: 978-0750628969.
L. N. Hand and J. D. Finch, "Analytical Mechanics", Cambridge University Press (1999), ISBN-10: 0521575729, ISBN-13: 978-0521575720. |
|
|
教科書・テキスト Textbook | | H. Goldstein, C. Poole and J. Safko, "Classical Mechanics", Pearson; 3rd edition (2013), ISBN-10: 1292026553, ISBN-13: 978-1292026558 |
|
|
課外学習等(授業時間外学習の指示) Study Load(Self-directed Learning Outside Course Hours) | | |
|
注意事項 Notice for Students | | |
|
他学科聴講の可否 Propriety of Other department student's attendance | | |
|
他学科聴講の条件 Conditions for Other department student's attendance | | |
|
レベル Level | | |
|
キーワード Keyword | | |
|
履修の際のアドバイス Advice | | |
|
授業開講形態等 Lecture format, etc. | | Hybrid or online only (will use Zoom or Teams) |
|
|
遠隔授業(オンデマンド型)で行う場合の追加措置 Additional measures for remote class (on-demand class) | | Please keep Zoom and Teams upgraded to the latest version. |
|
|