Cynthia Vaskis

SLM521 Spring 2004

Dropin #2 Assignment

4/2/04

File: Answers2.htm

Lesson Title: Math Calculations to Rotate an Object in 3D Space – Answers from Drop-in 2 top page

a) Elliptical, even the circular orbit is a special case of the ellipse where the two foci are the same point.

b) First, to point its antennas to communicate with Earth; second, to keep its solar arrays in view of the sun; and third, to point its star tracker or telescope to look for stars to determine the object’s orientation or attitude.

c) The state vector and the mathematician Kepler.

d) You can multiply the matrices M(Yaw) times M(Pitch) times M(Roll) together first as long as the order of the matrices is maintained where the first matrix is the right-most one in the equation. The resulting M(Full Rotation) matrix will be the same and can be used to multiply the object’s Point vectors.

e) The Mars rovers, Spirit and Opportunity, use math models to calculate how to move their research arms to take test samples of the soil and rocks on Mars. The automobile industry uses robotic arms to build cars. The robotic arms are controlled by math models with rotational matrices. Medical disease control centers use robotic appendages which employees control through windowed rooms to handle dangerous materials. Welding plants use robotic welders which have to be programmed to perform rotations of their robotic appendages for dangerous tasks.