Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HC021000 Specialized Education 解析力学 カイセキリキガク Analytical Mechanics NOHARA MINORU ノハラ　ミノル Higashi-Hiroshima 2nd-Year,  First Semester,  First Semester (1st) Thur5-6：SCI E102 Lecture The lecture is given mostly by writing on blackboard. Quiz and homework will be given occasionally to enhance comprehension. 2.0 B : Japanese／English 3 : Undergraduate High-Intermediate 25 : Science and Technology 06 : Physics Variation method, Principle of least action, Lagrange’s equation, Symmetry, Conservation law, Hamiltonian 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. Physics（Knowledge and Understanding）・Knowledge and understanding of physical mathematics, mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics. 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. lesson1 Principle of least action, variational method, and Euler-Lagrange equationlesson2 Application of Euler-Lagrange equationlesson3 Application of variational methodlesson4 Symmetry and Lagrangian: Time translational symmetrylesson5 Symmetry and Lagrangian: Spatial translational and rotational symmetrieslesson6 Symmetry and conservation laws: Noether’s theoremlesson7 Symmetry and conservation laws: Conservation laws of energy, momentum, and angular momentumlesson8 Mid-term summary of the class so far and Mid-term examlesson9 Constrained system and Lagrange’s method of undetermined multiplierslesson10  Application of Lagrange’s method of undetermined multiplierslesson11 Coupled oscillationlesson12 Hamilton’s equation of motionlesson13 Poisson bracketlesson14 Canonical transformationlesson15 Hamilton-Jacobi’s theory. (The final exam will be given during the 16th lesson.)There will be mid-term and final examinations. There is no specified textbook. The book of reference is, for instance, as follow: “Mechanics” by L. D. Landau and E. M. Lifshitz We mainly use board writing, but we may distribute graphs and calculation processes as materials. 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. Have acquired the credit of mechanics. Mid-term and final exams. 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. 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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