Course Objectives
(1) Understand the Lagrangian formulation
(2) Understand and obation the methods of analysis by Lagrangian formulation.
(3) Understand the Hamiltonian formulation (canonical formulation).
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Fully understand the formulation of Lagrangian mechanics. | Understand the formulation of Lagrangian mechanics. | Do not understand the formulation of Lagrangian mechanics. |
| Achievement 2 | Fully understand the methods of analysis by Lagrangian formulation. | Understand the methods of analysis by Lagrangian formulation. | Do not understand the methods of analysis by Lagrangian formulation. |
| Achievement 3 | Fully understand the formulation of Hamiltonian mechanics. | Understand the formulation of Hamiltonian mechanics. | Do not understand the formulation of Hamiltonian mechanics. |
Assigned Department Objectives
Teaching Method
Outline:
By using the Newton's equations, various motion can be described and investigated mathematically. It is useful and powerfull in various engineering fields. However, it is necessary to consider a coordinate system for each object to be handled and consider how the equation of motion in its coordinate system will be. By using the analytic mechanics, such problems can be avoided and general prescriptions with good prospects can be obtained.
Style:
Outline and necessary subjects will be illustrated through theory lectures, followed by practice lectures.
The students are expected to solve the practice problems with their own hands, and to explain their solutions to other students easy to understand.
Notice:
This course's content will amount to 90 hours of study in total. These hours include the learning time guaranteed in classes and the standard self-study time required for pre-study / review, and completing assignment reports. Be aware that class time makes up a small percentage of the overall expected learning time, and students are advised to thoroughly pre-study or review.
Students who miss 1/5 or more of classes will not be eligible for evaluation.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
The principle of least action |
Learn the basics about the principle of least action.
|
| 2nd |
Examples of Lagrange's equations I |
Learn and solve the examples of Lagrange's equations
|
| 3rd |
The principle of virtual work and d'Alembert's principle |
Learn the basics about the principle of virtual work and d'Alembert's principle.
|
| 4th |
Examples of Lagrange's equations II |
Learn and solve the examples of Lagrange's equations
|
| 5th |
Conservation laws |
Learn the basics of conservation laws.
|
| 6th |
Examples of conservation laws |
Learn and solve the examples of conservation laws.
|
| 7th |
Integration of the equations of motion |
Learn the basics of integration of the equations of motion.
|
| 8th |
Examples of integration of the equations of motion |
Learn and solve the examples of integration of the equations of motion
|
| 2nd Quarter |
| 9th |
Small oscilations |
Learn the basics of small oscilations.
|
| 10th |
Examples of small oscilations |
Learn and solve the examples of small oscilations.
|
| 11th |
Motion of a rigid body |
Learn the basics of motion of a rigid body.
|
| 12th |
Examples of rigid body motions |
Learn and solve the examples of rigid body motions
|
| 13th |
Motion in a non-inertial frame of reference |
Learn the basics of motion in a non-inertial frame of reference.
|
| 14th |
Example of motion in a non-inertial frame of reference |
Learn and solve the example of motion in a non-inertial frame of reference.
|
| 15th |
Canonical equations |
Learn the basics of canonical equations.
|
| 16th |
Final exam
|
|
Evaluation Method and Weight (%)
| Examination | Exercise | Total |
| Subtotal | 70 | 30 | 100 |
| Basic Proficiency | 0 | 0 | 0 |
| Specialized Proficiency | 70 | 30 | 100 |
| Cross Area Proficiency | 0 | 0 | 0 |