This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ve to find
the products of the basis unit vectors. Because of the antisymmetry property we get A ä A = 0. It follows then that `` `` ``
0 = x ä x = y ä y = z ä z. Chapter I  Rotational Dynamics and Equilibrium  3 Using our definition of the cross product we can see that the cross product of two perpendicular unit vectors is a third unit vector perpendicular
to the two. `
``
`
A ä B = A B sin q u ï v ä w = 1 ÿ 1 ÿ 1 u
`
`
`
`
The cross product of the unit vectors x and y is thus a unit vector perpendicular to the xy plane. This is either z or z. We insist that our
coordinate system is righthanded; this means that `` `
x ä y = z.
For the other combinations of unit vectors there is a simple rule to keep track of their cross products. Arrange x, y and z around a circle. x
z y If the order of the three coordinates has the same sense of rotation as x, y, z it gains a positive sign. If opposite it gets a minus sign. `` ` `` `
y ä z = x, z ä x = y ,
``
` ``
`
``
`
y ä x = z, x ä z = y and z ä y = x
We can put all this together and get the cross product in terms of components. `
`
`
`
`
`
A ä B = I A x x + A y y + A z zM ä I B x x + B y y + B z zM
`
`
`
= x I A y Bz  Az B y M + y H Az B x  A x Bz L + z I A x B y  A y B x M
The determinant method is a common way to write this....
View
Full
Document
This document was uploaded on 02/26/2014 for the course PHYS 2425 at Blinn College.
 Summer '08
 Honan
 Physics, Force

Click to edit the document details