2022 Analytical Mechanics(Lecture)

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Academic unit or major
Undergraduate major in Physics
Suyama Teruaki 
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(W621)  Thr3-4(W621)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

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.

Student learning outcomes

- 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.


Lagrangian, Hamiltonian, symmetry

Competencies that will be developed

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/Required learning

  Course schedule Required learning
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

Out-of-Class Study Time (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.



Reference books, course materials, etc.

Landau-Lifshitz, Mechanics

Assessment criteria and methods

final examination

Related courses

  • PHY.Q207 : Introduction to Quantum Mechanics

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

Concurrent registration for the exercise class is highly recommended.

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