### 2021　Rigid body dynamics

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Undergraduate major in Transdisciplinary Science and Engineering
Instructor(s)
Takahashi Kunio
Course component(s)
Lecture    (対面/ZOOM)
Day/Period(Room No.)
Tue1-2(S611)  Fri1-2(S611)
Group
-
Course number
TSE.A301
Credits
2
2021
Offered quarter
3Q
Syllabus updated
2021/9/28
Lecture notes updated
-
Language used
English
Access Index ### Course description and aims

This course gives knowledge and skills of the rigid body dynamics including the motion of point mass observed from moving coordinates and the motion of rigid body, mainly for the students who are learning the transdisciplinary science and engineering.
The aim is to let the students to understand the logic of the dynamics of the rigid body and to learn the skills for applications, based on the basic dynamics learnt in the lectures of the first year. Because recent engineering and technology are not limited in a discipline, the understanding of them will be helpful for global engineers, who will develop the future of the world and need wide-ranged knowledge and skills to solve complicated problems.

### Student learning outcomes

Out-comes are the knowledge and the skills
1) To derive the equation of motion of point mass observed from moving coordinate and to utilize it for applications.
2) To explain the mechanism of the centrifugal force and the Coliori’s force
3) To derive the equation of motion of rotating rigid body and to utilize it for applications
4) To derive the equation of motion of rotating rigid body observed from moving coordinates and to utilize it for applications

### Keywords

Equation of motion, absolute coordinate, moving coordinate, rotational motion of rigid body, Inertia tensor, Foucault’s pendulum, gyro effect, precession of spinning top

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

Lecture and exercises

### Course schedule/Required learning

Course schedule Required learning
Class 1 Guidance, Equation of motion of point mass observed from translating coordinate How to learn, Derivation of equation
Class 2 Equation of motion of point mass observed from rotating coordinate Derivation of equation, logic
Class 3 Application : motion observed from merry-go-round and earth’s surface Application of the equation, Physical meaning
Class 4 Application : Zero-gravity by free fall ( centrifugal force and Corioli’s force ) Application of the equation, Physical meaning
Class 5 Application : Foucault’s pendulum Application of the equation, Physical meaning
Class 6 Equation of motion of point mass observed from moving (translating and rotating) coordinate Derivation of equation, logic
Class 7 Equation of motion of rotating rigid body around a fixed axis Derivation of equation, logic
Class 8 Application : pulleys and wheels Application of the equation, Physical meaning
Class 9 Equation of motion of rotating rigid body around an arbitrary axis Derivation of equation, logic
Class 10 Definition and physical meaning of torque, inertia tensor, angular moment and energy logic
Class 11 Application : inertia tensor ( moment of inertia, product of inertia ), Gyro effect Application of the equation, Physical meaning
Class 12 Diagonalization of inertia tensor ( principal axes and principal moments ) Application of the equation, Physical meaning
Class 13 Equation of motion of rotating rigid body observed from moving coordinate Derivation of equation, logic
Class 14 Application : Precession of spinning top Application of the equation, Physical meaning

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

pdf in OCW

pdf in OCW

### Assessment criteria and methods

attendance 10% + exercise 20% + final exam. 70% ( + bonus point for contribution to the lecture )
（may be changed according to COVID19）

### Related courses

• LAS.P101 ： Fundamentals of Mechanics 1
• LAS.P102 ： Fundamentals of Mechanics 2
• LAS.M105 ： Calculus II
• LAS.M106 ： Linear Algebra II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

The followings should be finished ;
LAS.P101 ： Fundamentals of Mechanics 1, LAS.P102 ： Fundamentals of Mechanics 2, LAS.M105 ： Calculus II, LAS.M106 ： Linear Algebra II 