HC021000 Analytical Mechanics

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HC021000 Subject Classification Specialized Education

Subject Name 解析力学

Subject Name
（Katakana）カイセキリキガク

Subject Name in
English Analytical Mechanics

Instructor NOHARA MINORU

Instructor
(Katakana) ノハラ　ミノル

Campus Higashi-Hiroshima Semester/Term 2nd-Year, First Semester, First Semester

Days, Periods, and Classrooms (1st) Thur5-6：SCI E102

Lesson Style Lecture Lesson Style
(More Details) 　

The lecture is given mostly by writing on blackboard.
Quiz and homework will be given occasionally to enhance comprehension.

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 06 : Physics

Eligible Students

Keywords Variation method, Principle of least action, Lagrange’s equation, Symmetry, Conservation law, Hamiltonian

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) In order to understand physics such as quantum mechanics and electromagnetism, you will learn the concepts and methods of analytical mechanics that are the basis of it.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Physics
（Knowledge and Understanding）
・Knowledge and understanding of physical mathematics, mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics.

Class Objectives
/Class Outline In mechanics, we described the motion of material points and rigid bodies starting from Newton’s equation of motion. In analytical mechanics, we will learn mor general forms of mechanics, starting from the “principle of least action”. First, we will learn Lagrangian and Lagrange-style mechanics starting from the principle of least action. After that, we will learn Hamilton-style mechanics. This will lead to future learning of quantum mechaniscs.

Class Schedule lesson1 Principle of least action, variational method, and Euler-Lagrange equation
lesson2 Application of Euler-Lagrange equation
lesson3 Application of variational method
lesson4 Symmetry and Lagrangian: Time translational symmetry
lesson5 Symmetry and Lagrangian: Spatial translational and rotational symmetries
lesson6 Symmetry and conservation laws: Noether’s theorem
lesson7 Symmetry and conservation laws: Conservation laws of energy, momentum, and angular momentum
lesson8 Mid-term summary of the class so far and Mid-term exam
lesson9 Constrained system and Lagrange’s method of undetermined multipliers
lesson10 Application of Lagrange’s method of undetermined multipliers
lesson11 Coupled oscillation
lesson12 Hamilton’s equation of motion
lesson13 Poisson bracket
lesson14 Canonical transformation
lesson15 Hamilton-Jacobi’s theory. (The final exam will be given during the 16th lesson.)

There will be mid-term and final examinations.

Text/Reference
Books,etc. There is no specified textbook. The book of reference is, for instance, as follow:
“Mechanics” by L. D. Landau and E. M. Lifshitz

PC or AV used in
Class,etc. 　

(More Details) We mainly use board writing, but we may distribute graphs and calculation processes as materials.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review It is important to be able to derive various physical laws and corresponding equations from the basic principles without resorting to memorization. For that purpose, it is effective to practice transforming the formula without looking at anything. It is also helpful to note the physical meaning of the equation.

Requirements Have acquired the credit of mechanics.

Grading Method Mid-term and final exams.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message Analytical mechanics is completely different from the physics that you learned in high school, and is full of real physics. I would like to continue the lecture while having fun together. Questions and requests are welcome.

Other We will present homework for preparation and review.

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	HC021000	Subject Classification	Specialized Education
Subject Name	解析力学
Subject Name （Katakana）	カイセキリキガク
Subject Name in English	Analytical Mechanics
Instructor	NOHARA MINORU
Instructor (Katakana)	ノハラ　ミノル
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, First Semester
Days, Periods, and Classrooms	(1st) Thur5-6：SCI E102
Lesson Style	Lecture	Lesson Style (More Details)
The lecture is given mostly by writing on blackboard. Quiz and homework will be given occasionally to enhance comprehension.
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	06 : Physics
Eligible Students
Keywords	Variation method, Principle of least action, Lagrange’s equation, Symmetry, Conservation law, Hamiltonian
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	In order to understand physics such as quantum mechanics and electromagnetism, you will learn the concepts and methods of analytical mechanics that are the basis of it.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Physics （Knowledge and Understanding）・Knowledge and understanding of physical mathematics, mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics.
Class Objectives /Class Outline	In mechanics, we described the motion of material points and rigid bodies starting from Newton’s equation of motion. In analytical mechanics, we will learn mor general forms of mechanics, starting from the “principle of least action”. First, we will learn Lagrangian and Lagrange-style mechanics starting from the principle of least action. After that, we will learn Hamilton-style mechanics. This will lead to future learning of quantum mechaniscs.
Class Schedule	lesson1 Principle of least action, variational method, and Euler-Lagrange equation lesson2 Application of Euler-Lagrange equation lesson3 Application of variational method lesson4 Symmetry and Lagrangian: Time translational symmetry lesson5 Symmetry and Lagrangian: Spatial translational and rotational symmetries lesson6 Symmetry and conservation laws: Noether’s theorem lesson7 Symmetry and conservation laws: Conservation laws of energy, momentum, and angular momentum lesson8 Mid-term summary of the class so far and Mid-term exam lesson9 Constrained system and Lagrange’s method of undetermined multipliers lesson10 Application of Lagrange’s method of undetermined multipliers lesson11 Coupled oscillation lesson12 Hamilton’s equation of motion lesson13 Poisson bracket lesson14 Canonical transformation lesson15 Hamilton-Jacobi’s theory. (The final exam will be given during the 16th lesson.) There will be mid-term and final examinations.
Text/Reference Books,etc.	There is no specified textbook. The book of reference is, for instance, as follow: “Mechanics” by L. D. Landau and E. M. Lifshitz
PC or AV used in Class,etc.
(More Details)	We mainly use board writing, but we may distribute graphs and calculation processes as materials.
Learning techniques to be incorporated
Suggestions on Preparation and Review	It is important to be able to derive various physical laws and corresponding equations from the basic principles without resorting to memorization. For that purpose, it is effective to practice transforming the formula without looking at anything. It is also helpful to note the physical meaning of the equation.
Requirements	Have acquired the credit of mechanics.
Grading Method	Mid-term and final exams.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	Analytical mechanics is completely different from the physics that you learned in high school, and is full of real physics. I would like to continue the lecture while having fun together. Questions and requests are welcome.
Other	We will present homework for preparation and review.
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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