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.
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
Equation of motion, absolute coordinate, moving coordinate, rotational motion of rigid body, Inertia tensor, Foucault’s pendulum, gyro effect, precession of spinning top
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Lecture and exercises
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 |
pdf in OCW
pdf in OCW
attendance 10% + exercise 20% + final exam. 70% ( + bonus point for contribution to the lecture )
（may be changed according to COVID19）
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