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Graduate School
Analytical Dynamics
Junichiro INOUE Professor
Department: School of Engineering / Graduate School of Engineering
Class Time:  2003 Fall Friday 
Recommended for:  Quantum Science and Energy Engineering students 
Course Overview
Course Aims
A general course of physics contains classical mechanics, electromagnetic dynamics, thermo dynamics, statistical mechanics and quantum mechanics. Analytical mechanics is reformulation of classical mechanics, which involve advanced mathematical approaches. The basics of classical mechanics are Newton's laws of motion, and they provide relationships between the motion of the body and the force acting on the body. However, Lagrangian mechanics and Hamiltonian mechanics can also provide the equivalent relationships. In this lecture we will focus on the application of Lagrangian mechanics and Hamiltonian mechanics for the complex system. We will also focus on the fundamental idea of classical mechanics and its relations to Lagrangian mechanics and Hamiltonian mechanics.
Key Features
Lecture is given based on the lecture notes distributed in the beginning of each class. This lecture involves with some basics of calculus 3 by 3 matrix operations. It is very important for students to derive the equation introduced in this class. Therefore exercise session will be given just after the lecture. Two teaching assistants will be organizing the exercise session, and there will be about hundred students. They will be ready to answer questions about the classes. Midterm exams are also given to make sure students understand the basics of Analytical Physics.
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Syllabus
Course Aims
We will be reviewing the Newton's second law and its application for the case of mass system for the first part of this course. We will then focus on the vibration of multidegreeoffreedom system and rigidbody dynamics. Furthermore we will learn about variational principles and canonical equations of motion, which are deeply related to the field of quantum mechanics.
Requirements and recommended courses
Mechanics 1, Mechanics 2, Calculus, Linear Algebra
Textbooks
Lecture notes are provided.
Assignments
Practice exercises on the last part of chapter are sometimes given for homework.
Course Schedule
Lecture notes consist of 11 chapters. The amount of material covered in this course is much considering that we only have 2.5 hour of class every week. Therefore, in order to enforce your ability for analytical physics, practice exercises on the last part of each chapter are highly recommended for the review.
Session  Chapter  Contents 

1  1st chapter Classical Newtonian mechanics  Review of Newton's laws of motion and its application for the one dimensional motion 
2  1st chapter Classical Newtonian mechanics continued  Equation of motion in polar coordinates and its application for the two dimensional motion 
3  2nd chapter Central force motion  General solution for the central force motion Example problems of the motion of planets 
4  3rd chapter Scattering problem  Scattering problem as one of the example of central force motion and its example problems 
5  4th chapter Lagrangian and Lagrange's equation  Introduction of Lagrangian and application of the Lagrange's equation. Advantages of Lagrange's equation 
6  5th chapter Microscopic vibration  Example problem on vibration motion and typical usage of Lagrangian. Microscopic vibration in multiple degree of freedom system. 
7  5th chapter Microscopic vibration continued  Example problems on vibration in multiple degree of freedom system and its characteristics 
8  6th chapter Motion of rigid body  Introduction of inertia tensor for the case of motion of rigid body Conservation of energy equation for the case of rigid body motion 
9  6th chapter Motion of rigid body continued   Method of calculating inertia tensor and inertia moment 
10  7th chapter Lagrangian of the rigid body and its Equation of motion  Equation of motion of the rigid body and its example problems. 
11  7th chapter Lagrangian of the rigid body and its Equation of motion continued.  More difficult example problems. 
12  8th chapter Euler angle and motion of the spinning top  Euler angle as the representation of rotating motion Example problems about spinning top 
13  9th chapter Variational principles  Variational principles, or the fundamental idea of deriving equation of state, and its practice problems The relation between variational principles and principle of least action 
14  10th chapter Principle of virtual work  Principle of virtual work Derivation of Lagrange's equation 
15  11th chapter Hamilton's principle  Derivation of Hamilton's principle from principle of least action Its relation to quantum physics 
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Class Materials
Lecture Handouts
Lecture Notes (PDF, 973KB)
Lecture notes are provided but only in Japanese. Lecture notes consist of 7 chapters containing example problems at the end of each chapter. I would like you to use these problems for your review.
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Page last updated February 11, 2009
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.