2017 Analytical Mechanics A

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Academic unit or major
Undergraduate major in Physics
Nishida Yusuke  Nasu Joji 
Course component(s)
Lecture / Exercise
Mode of instruction
Day/Period(Room No.)
Mon3-6(H112)  Thr3-4(H112)  
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 and concrete problems are given and then solved by students in exercise 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
Class 15 Periodic Motion and Canonical Variables



Reference books, course materials, etc.

Lecture notes will be distributed via OCW-i.
Problem sets will be distributed.

Assessment criteria and methods

Evaluated based on presentation, mini-exams, and reports in exercise classes (~40%) and final examination (~60%).

Related courses

  • PHY.Q207 : Introduction to Quantum Mechanics

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


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