2019 Mechanics (EPS course)

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Academic unit or major
Undergraduate major in Earth and Planetary Sciences
Imaeda Yusuke  Sato Bunei  Okuzumi Satoshi  Hirano Teruyuki 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Tue3-6(I123)  Fri3-6(I123)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

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/Required learning

  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 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



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)

Assessment criteria and methods

Student performance will be assessed by the combination of the exercise (40%), and the final exam in the 15th lecture (60%).

Related courses

  • PHY.Q206 : Analytical Mechanics

Prerequisites (i.e., required knowledge, skills, courses, etc.)


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