Analytical Mechanics I(2.0 credits) | ||||
| Code | : | 10155 | ||
| Course Type | : | Basic Specialized Courses | ||
| Class Format | : | Lecture | ||
| Course Name | : | Chemistry | Fundamental and Applied Physics | |
| Starts 1 | : | 2 Autumn Semester | 2 Autumn Semester | |
| Elective/Compulsory | : | Elective | Compulsory | |
| Lecturer | : | SHIGEMORI Masaki Designated Professor | ||
| •Course Purpose |
| This is the first of two courses in analytical mechanics. Analytical mechanics abstracts from Newtonian mechanics and generalizes it to a versatile framework that can be applied to various areas of physics, such as quantum mechanics, statistical mechanics, and relativity. After a survey of elementary principles, we discuss the core concepts of Lagrangian and Hamiltonian mechanics, with special emphasis on symmetry principles, followed by some explicit examples.
A student who successfully completes this course will be able to: - Understand the notions and procedures of the calculus of variations - Write down the Lagrangian of a mechanical system in terms of generalized coordinates and describe its motion using the Euler-Lagrange equations - Understand the relation between symmetries and conservation laws and write down the associated conserved quantities - Describe the motion of mechanical systems using Hamiltonians - Describe motion in central force problem using effective potential |
| •Prerequisite Subjects |
| Calculus I & II, Fundamentals of Physics I &II, and concurrent registration of Mathematical Physics I & II |
| •Course Topics |
| 1. Survey of elementary principles
2. Variational principles and Lagrangian mechanics 3. Symmetries and conservation laws 4. Hamiltonian mechanics 5. Central force problem It is desirable to read a textbook or reference materials before a class |
| •Textbook |
| H. Goldstein, C. Poole and J. Safko, "Classical Mechanics", Pearson; 3rd edition (2013), ISBN-10: 1292026553,
ISBN-13: 978-1292026558 |
| •Additional Reading |
| L. D. Landau and E. M. Lifschitz, "Mechanics: Volume 1 (Course of Theoretical Physics)", Butterworth-Heinemann; 3rd
edition (1976), ISBN-10: 0750628960, ISBN-13: 978-0750628969. L. N. Hand and J. D. Finch, "Analytical Mechanics", Cambridge University Press (1999), ISBN-10: 0521575729, ISBN-13: 978-0521575720. |
| •Grade Assessment |
| Attendance/Quizzes 10%, homework 30%, midterm 30%, final exam 30%
The “Absent” grade is reserved for students who withdraw by the deadline. After that day, a letter grade will be given based on the assessment during the semester. |
| •Notes |
| Hybrid or online only (will use Zoom or Teams) |
| •Contacting Faculty |
| Join and check the NUCT website for Analytical Mechanics (AM1) for announcements. |