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 abundant exercise 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
|✔ Specialist skills||Intercultural skills||Communication skills||✔ Critical thinking skills||✔ Practical and/or problem-solving skills|
To be announced.
|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||Kepler Motion||motion in a central force field, Kepler's laws|
|Class 6||Micro Vibration||one-dimensional and multi-dimensional vibrations|
|Class 7||mid-term exam / exercise||applied problems|
|Class 8||Normal Vibration||eigenfrequency|
|Class 9||Motion in a Rotating Frame||force of inertia|
|Class 10||Rigid-body Motion||rotational energy, moment of inertial|
|Class 11||Variation Principle||functional, Euler equation|
|Class 12||Hamilton Formalism and Canonical Equation||Legendre transformation, Hamiltonian|
|Class 13||Canonical Transformation||Hamilton-Jacobi equation|
|Class 14||Exercise of Analytical Mechanics I||solve problems using Lagrange and Hamiltonian formalism|
|Class 15||Exercise of Analytical Mechanics II||solve problems using Lagrange and Hamiltonian formalism|
Yasushi Suto, "Analytical Mechanics and Quantum Mechanics", University of Tokyo Press (Japanese)
Isao Imai, "Exercise in Mechanics", Science Press (Japanese)
Landau-Lifshitz, "Mechanics, Third Edition: Volume 1" (Course of Theoretical Physics), Butterworth-Heinemann (English or Japanese)
Student performance will be assessed by the combination of the exercise attendance/presentation, mid-term exam (one third), and final exam (one third).