1. Ch1.4e (Ch1.5) Triple Scalar Product and Triple Vector Product
講者： 許永昌 老師

2. Contents The angular momentum and the kinetic energy of a particle
Triple Scalar Product
A(BC)
Triple Vector Product
A(BC)
Summary

3. L and K of a particle
Assume a particle mass m whose angular velocity is w and its position is r at an instant. What is the angular momentum and the kinetic energy at this instant?
L=rp=mr(wr)=mr2w –m(rw)r
K= ½mv2=½m(wr)(wr)
=½mr2w2-½m(wr)2
=½Izzw2. (if w//z)
 Exercise & w r

4. Triple Scalar Product A(BC)= B(CA)= C(AB)= A(BC)=
A(BC)= () volume of parallelepiped defined by A, B and C.
Code: example_cross_product.m

5. Triple Vector Product (P28, P32e)
No Commutative relation: A(BC) (AB)C.
E.g.
A(BC)=(AC)B-(AB)C.
Proof:
A(BC) should be perpendicular to A and BC, therefore, A(BC)=uB+vC and A(uB+vC)=0.
Therefore, A(BC)=w( (AC)B-(AB)C ).
w is independent of A (owing to A=SiAiûi), and is also independent of B and C.

6. Summary
Because vectors are independent of the coordinates, a vector equation is independent of the particular coordinate system. The coordinate system only determines the components.
Triple Scalar Product: V3V0 (scalar)
A(BC)= B(CA)= C(AB)
Triple Vector Product: V3V
A(BC)=(AC)B-(AB)C

7. Homeworks 1.4.1e (1.5.2) 1.4.2e (1.5.3) 1.4.3e (1.5.5) 1.4.4e (1.5.6)