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
|✔ 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 I||motion in a central force field|
|Class 6||Kepler Motion II||Kepler's laws|
|Class 7||Micro Vibration||one-dimensional and multi-dimensional vibrations|
|Class 8||Normal Vibration||eigenfrequency|
|Class 9||Motion in a Rotating Frame||force of inertia|
|Class 10||Rigid-body Motion I||rotational energy, moment of inertial|
|Class 11||Rigid-body Motion II||rotational energy, moment of inertial|
|Class 12||Variation Principle||functional, Euler equation|
|Class 13||Hamilton Formalism and Canonical Equation||Legendre transformation, Hamiltonian|
|Class 14||Canonical Transformation||Hamilton-Jacobi equation|
|Class 15||Exercise of Analytical Mechanics||solving problems using Lagrange and Hamiltonian formalism|
Isao Imai, "Exercise in Mechanics", Science Press (Japanese)
Yasushi Suto, "Analytical Mechanics and Quantum Mechanics", University of Tokyo Press (Japanese),
Kenichi Kubo, "Analytical Mechanics", Shokabo (Japanese)
Student performance will be assessed by the combination of the mid-term exam (30%), final exam (30%), and five reports (40%).