Course title
応用力学   [Advanced Mechanics]
Course category	common courses	Requirement		Credit	2
Department		Year	～	Semester	Fall
Course type	Fall	Course code	1060485
Instructor(s)
村山 能宏, 室尾 和之   [MURAYAMA Yoshihiro, MUROO Kazuyuki]
Facility affiliation	Faculty of Engineering	Office		Email address

Course description

Analytical mechanics is a generalized form of classical mechanics, which is derived based on the principle of least action. In the first half of this course, students will learn what is "principle of least action". And then students will learn Lagrangian dynamics, which is a consequence of application of principle of least action to Newton dynamics. In the last half, students will learn Hamiltonian dynamics, derived from Lagrangian dynamics and application to quantum mechanics and statistical mechanics.

Expected Learning

1. Students will be able to apply analytical mechanics to various problems in classical mechanics. 2. Students will be able to understand the fundamental concept of dynamical system.

Course schedule

Week 1: What is analytical mechanics? Week 2: Calculus of variations Week 3: Brachistochrone curve Week 4: Method of Lagrange multipliers Week 5: Hamilton’s principle (Principle of least action) Week 6: Lagrangian Mechanics (Euler-Lagrange equation) Week 7: Hamiltonian mechanics Week 8: Non-equilibrium system and oscillations Week 9: Dynamical system Week 10: Oscillator under external force Week 11: Stability of solutions (Linear stability analysis) Week 12: Non-linear oscillator under external force Week 13: Bifurcation of solutions Week 14: Oscillatory and excitable (Belousov?Zhabotinsky reaction) Week 15: Summary of this course

Prerequisites

Required Text(s) and Materials

References

Assessment/Grading

Message from instructor(s)

Course keywords

Office hours

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

7/17/2018 1:43:58 PM