1. Rotation of Coordinate Systems A x z y x* z* y* Rotation Matrix

2. Properties of a Rotation Matrix Rotation around z axis: q z x y x* y*

3. Euler Angles x z y x* z*y* x’ q f y Steps: 1.Rotate around z such that x’ is perpendicular to z* 2.Rotate around x’ by q 3.Rotate around z* by y

4. Euler Angles (continued)

5. Rotating System x z y x* z*y* x’ q f (t) y Now the rotation around z* is a function of time

6. Special Matrix Totally antisymmetric tensor

7. Cross Product Matrix x y z w wzwz f

8. Second Derivative Centripetal Acceleration Appears to throw object outward For position vector: Coriolis Acceleration Appears to push object perpendicular to velocity

9. Stationary Orbit Satellite 0 0 0 For stationary orbit: at equator!

10. Falling Body Observed on Earth Time to fall: Apparent velocity as a function of height: Distance:

11. Falling Body Observed in Space Ellipitical Orbit Point of Impact – east and south Distance: Motion of building during fall See Mathematica notebook

12. Coriolis Force Derivation Time of fall: Vertical velocity: Horizontal acceleration: Horizontal velocity: Horizontal position: