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2025 (Current Year) Faculty Courses School of Science Undergraduate major in Earth and Planetary Sciences

Mechanics (EPS course)

Academic unit or major
Undergraduate major in Earth and Planetary Sciences
Instructor(s)
Yusuke Imaeda / Taishi Nakamoto
Class Format
Lecture/Exercise (Face-to-face)
Media-enhanced courses
-
Day of week/Period
(Classrooms)
3-6 Tue (I1-255(I123)) / 3-6 Fri (I1-255(I123))
Class
-
Course Code
EPS.B203
Number of credits
220
Course offered
2025
Offered quarter
2Q
Syllabus updated
Mar 19, 2025
Language
Japanese

Syllabus

Course overview and goals

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.

Course description and aims

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.

Keywords

Lagrange formalism, variation principle, Hamiltonian formalism, Canonical Transformation

Competencies

  • Specialist skills
  • Intercultural skills
  • Communication skills
  • Critical thinking skills
  • Practical and/or problem-solving skills

Class flow

This course consists of concurrent lectures and exercises.

Course schedule/Objectives

Course schedule Objectives
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

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

None

Reference books, course materials, etc.

■ 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)

Evaluation methods and criteria

Overall evaluation will be based on 40% for work on exercises and 60% for the final report.

Related courses

  • PHY.Q206 : Analytical Mechanics

Prerequisites

None