Course Objectives
Learning purposes :
Understand Lagrange's equation of motion and solve applied problems as the basis of analytical mechanics. In addition, by understanding Hamilton's canonical equations and solving applied problems, students will learn calculation methods.
Course Objective :
1. Understand Lagrange's equation of motion and solve related problems.
2. Understand Hamilton's canonical equations and solve related problems.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Can create answers to most of the problems dealt with in class about Lagrange's equation of motion. | Can create answers to problems dealt with in class about Lagrange's equation of motion. | Has not reached the left. |
| Achievement 2 | Can create answers to most of the problems dealt with in class about Hamilton's canonical equations. | Can create answers to problems dealt with in class about Hamilton's canonical equations. | Has not reached the left. |
Assigned Department Objectives
Teaching Method
Outline:
General or Specialized : Specialized
Field of learning : Physics
Required, Elective, etc. : Elective subjects
Basic disciplines: Mathematical science / physics / general physics
Relationship with Educational Objectives : This subject corresponds to the learning objective of each engineering department, "(1) Acquire knowledge about natural science subjects centered on mathematics and physics, and acquire the ability to apply it as basic knowledge about each engineering."
Relationship with JABEE programs : The main goal of learning or education in this subject is "(A) Deepening of basic knowledge about technology, A-1: Acquiring knowledge in a wide range of natural sciences as basic knowledge about engineering, and can be explained. "
Class outline : Analytical mechanics provides a method for systematically dealing with classical mechanics, and is also important for studying quantum mechanics and the theory of relativity in earnest. This course focuses on the basics of analytical mechanics, including the Lagrangian and Hamiltonian forms.
Style:
Course method:
Lecture-style lessons will be conducted and exercises will be conducted as appropriate. In the exercise, students will be asked to write a board and explain the answers. Impose an assignment report and proceed with the lesson while confirming the degree of understanding of the students.
Grade evaluation method:
Exams (60%) + Exercises (40%) .
Supplementary classes and re-taking exams will be imposed on those with poor grades, and the results of the regular exam will be replaced with a maximum of 60 points.
Notice:
Precautions on the enrollment :
This subject is a "subject that requires study outside of class hours". Classes are offered for 15 credit hours per credit, but 30 credit hours are required in addition to this. Follow the instructions of teacher for these studies.
Course advice :
Read the textbook well. Also, be sure to submit the assignment report by the deadline.
Basic subjects :
General Physics (3rd year), Differential and Integral I (2), Differential and Integral II (3), Fundamental Differential Equations (3)
Related subjects :
Quantum Science (5th year), Electromagnetism (4), Modern Physics (4), Condensed Matter Physics (4), Mathematics subject
Attendance advice :
Calculate and understand the mathematical formulas. If students are operating e-mail etc. during class, may be asked to leave the room. If student join the class starts within 25 minutes, it will be lateness, and 3 times lateness will result in 1 absence.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 2nd Semester |
| 3rd Quarter |
| 1st |
・ Other than mathematics and physics science programs: Not offered
・ Mathematics and Physics Program: Guidance |
Guidance
|
| 2nd |
Virtual Work Principle and D'Alembert's Principle |
Understand the principles of virtual work and D'Alembert's principles.
|
| 3rd |
Hamilton's principle |
Understand Hamilton's principle, action integral, and Lagrangian.
|
| 4th |
Polar coordinate format |
Understand the relationship between Cartesian coordinates and polar coordinates, and derive a transformation formula.
|
| 5th |
Lagrange's equation of motion |
Understand Lagrange's equation of motion and generalized coordinates.
|
| 6th |
Example using Lagrange's equation of motion |
Work on some examples.
|
| 7th |
Hamilton's equations |
Understand generalized momentum, Hamiltonian, Hamilton's equations, and canonical variables.
|
| 8th |
2nd term midterm exam (above content) |
Requires a score of 60 points or higher.
|
| 4th Quarter |
| 9th |
Return of answers for the 2nd term midterm exam. exam commentary. |
Review.
|
| 10th |
Canonical transformation |
Understand canonical transformation.
|
| 11th |
Variational principle by Hamiltonian |
Understand the variational principle and generating function.
|
| 12th |
Infinitesimal canonical transformation |
Understand infinitesimal canonical transformation.
|
| 13th |
Conserved quantity and generating function |
Understand conserved quantities and generating functions.
|
| 14th |
Noether's theorem |
Understand Noether's theorem.
|
| 15th |
2nd term final exam (contents after the 2nd term midterm exam) |
Requires a score of 60 points or higher.
|
| 16th |
Return of answers for the 2nd term final exam. exam commentary. |
Review.
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 60 | 0 | 0 | 0 | 40 | 0 | 100 |
| Basic Proficiency | 35 | 0 | 0 | 0 | 25 | 0 | 60 |
| Specialized Proficiency | 25 | 0 | 0 | 0 | 15 | 0 | 40 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |