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

EnglishAnalytical 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 OutlineIn 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

ReviewIt 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.