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.
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.
Lagrange formalism, variation principle, Hamiltonian formalism, Canonical Transformation
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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- | - | ✔ | ✔ | ✔ |
This course consists of concurrent lectures and exercises.
Course schedule | Required learning | |
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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 I | Solve problems using Lagrange and Hamiltonian formalism |
Class 14 | Exercise of Analytical Mechanics II | Solve problems using Lagrange and Hamiltonian formalism |
Class 15 | Examination | Examination |
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■ 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)
Student performance will be assessed by the combination of the exercise (40%), and the final exam in the 15th lecture (60%).
None