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2025 (Current Year) Faculty Courses School of Science Undergraduate major in Physics

Analytical Mechanics(Lecture)

Academic unit or major
Undergraduate major in Physics
Instructor(s)
Teruaki Suyama
Class Format
Lecture (Face-to-face)
Media-enhanced courses
-
Day of week/Period
(Classrooms)
3-4 Mon (WL2-101(W611)) / 3-4 Thu (WL2-101(W611))
Class
-
Course Code
PHY.Q206
Number of credits
200
Course offered
2025
Offered quarter
2Q
Syllabus updated
Apr 2, 2025
Language
Japanese

Syllabus

Course overview and goals

Analytical mechanics is the mathematically sophisticated reformulation of Newtonian mechanics and consists of Lagrangian mechanics and Hamiltonian mechanics. Not only does analytical mechanics enable us to solve problems efficiently, but it also opens up a route leading to quantum mechanics.
The objective of this course is to learn the following subjects in Lagrangian mechanics and Hamiltonian mechanics.

Course description and aims

- Being able to express and solve problems of mechanics with the use of Lagrangian and Hamiltonian.
- Being able to explain roles of symmetry in physics.

Keywords

Lagrangian, Hamiltonian, symmetry

Competencies

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

Class flow

Basic concepts and formulations are explained in lecture classes.

Course schedule/Objectives

Course schedule Objectives
Class 1

Equations of Motion and Coordinate Systems

Understand contents and results in each class and should be able to derive and explain them by oneself.
Also, be able to solve related concrete problems.

Class 2

Euler-Lagrange Equation

Class 3

Generalized Coordinates and Covariance

Class 4

Principle of Least Action

Class 5

Construction of Lagrangians

Class 6

Symmetries and Conversation Laws

Class 7

Treatment of Constraints

Class 8

Small Oscillations

Class 9

Phase Space and Canonical Equations

Class 10

Canonical Transformations

Class 11

Liouville's Theorem

Class 12

Infinitesimal Transformations and Conserved Quantities

Class 13

Poisson Bracket

Class 14

Hamilton-Jacobi Equation

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content.
They should do so by referring to textbooks and other course material.

Textbook(s)

None.

Reference books, course materials, etc.

Landau-Lifshitz, Mechanics

Evaluation methods and criteria

final examination

Related courses

  • PHY.Q207 : Introduction to Quantum Mechanics

Prerequisites

Concurrent registration for the exercise class is highly recommended.