授業の目的 【日本語】
Goals of the Course(JPN) | | |
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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. |
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到達目標 【日本語】
Objectives of the Course(JPN) | | |
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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 |
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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 |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | | Calculus I & II, Fundamentals of Physics I &II, and concurrent registration of Mathematical Physics I & II |
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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% |
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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 |
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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. |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | |
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使用言語
Language Used in the Course | | |
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授業開講形態等
Lecture format, etc. | | | Hybrid or online only (will use Zoom or Teams) |
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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. |
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