2017 Exercises in Classical Mechanics

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Nishida Yusuke  Nasu Joji 
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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 / Euler-Lagrange Equation Be able to solve concrete problems related to contents in each class.
Class 2 Generalized Coordinates and Covariance / Principle of Least Action
Class 3 Construction of Lagrangians / Symmetries and Conversation Laws
Class 4 Treatment of Constraints / Small Oscillations
Class 5 Phase Space and Canonical Equations / Canonical Transformations
Class 6 Liouville's Theorem / Infinitesimal Transformations and Conserved Quantities
Class 7 Poisson Bracket / Hamilton-Jacobi Equation
Class 8 Periodic Motion and Canonical Variables



Reference books, course materials, etc.

Problem sets will be distributed.

Assessment criteria and methods

Evaluated based on presentation, mini-exams, and term papers.

Related courses

  • ZUB.Q203 : Classical Mechanics
  • ZUB.Q204 : Quantum Mechanics I

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

Concurrent registration for the lecture class is highly recommended.

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