2019 Analytical Mechanics

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Academic unit or major
Undergraduate major in Physics
Instructor(s)
Yamaguchi Masahide  Watabiki Yoshiyuki 
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Mon3-4(H112)  Mon5-6(H102,H104)  Thr3-4(H112)  
Group
-
Course number
PHY.Q206
Credits
3
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/4/4
Lecture notes updated
-
Language used
Japanese
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.

Keywords

Lagrangian, Hamiltonian, symmetry

Competencies that will be developed

Intercultural skills Communication skills Specialist 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

Textbook(s)

None.

Reference books, course materials, etc.

Problem sets will be distributed.

Assessment criteria and methods

final examination, attendance and answer in the class, and report

Related courses

  • PHY.Q207 : Introduction to Quantum Mechanics

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

None.

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