1. Introduction to physics

2. Lecture 21 Gyro and Statics
Motion of a gyro
Statics
Virtual work

3. Moving a spinning wheel

4. A top

5. Gyroscopic precession
The precession of a gyroscope shows up in many “common” situations.

6. Actual motion of a Gyro, nutation
When we let go of a ryro, it first fall, and at the same time, process. It falls below the average procession line and then comes up again, and falls again in the vertical direction. The oscillation damps out eventually, one has in the end the pure procession.

7. Static equilibrium of rigid body
Mechanism of Confinement
Static equilibrium of rigid body
Dynamical equations of rigid body
Center of mass is at rest
No rotation
Mechanism of Confinement

8. Lever 𝐹
𝑙 1
𝐹− 𝑚 1 𝑔− 𝑚 2 𝑔=0
𝑚 1 𝑔 𝑙 1 − 𝑚 2 𝑔 𝑙 2 =0
𝑚 2 𝑔
𝑚 1 𝑔

10. View point of energy Energy conservation 𝐸=𝑇+𝑉=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
No kinetic energy 𝑇=0
When energy is 𝐸 1 or 𝐸 2 , the system is in the equilibrium state
Condition of equilibrium is the potential energy is at local minimum (stable equilibrium) or maximum (unstable equilibrium)

11. Stable equilibrium

12. Unstable equilibrium

13. Shape of hanging bridge

14. Protein Structure Prediction

16. Mechanism of Confinement
A elastic ring on a cone a h
Mechanism of Confinement

17. Mechanism of Confinement
Virtual displacement （虚位移）: displacement under constraint within the variation of time dt=0
Real displacement
Virtual work（虚功）:
Ideal constraint（理想约束）:
Virtual displacement
Mechanism of Confinement

18. Constraint forces 𝐹 𝑐𝑖 and other forces 𝐹 𝑖
Total virtual work
𝛿𝑊= Σ 𝑖 ( 𝐹 𝑖 + 𝐹 𝑐𝑖 ) ∙𝛿 𝑟 𝑖
Ideal constraint
Σ 𝑖 𝐹 𝑐𝑖 ∙𝛿 𝑟 𝑖 =0
Static equilibrium
Σ 𝑖 𝐹 𝑖 + 𝐹 𝑐𝑖 =0→ Σ 𝑖 𝐹 𝑖 ∙𝛿 𝑟 𝑖 =0

19. Mechanism of Confinementl1 l2 q1 q2
m1g
m2g
Mechanism of Confinement