Euler's Rotation Theorem: Rotating objects in 3-space

The purpose of this thesis is to explore Euler's Rotation Theorem as it applies to the rotation of objects along various paths. Matrices can be used to represent these rotations along with the equation for a specific sphere. After these matrices are selected Maple programming will be used to calculate and further animate the rotation of a sphere (the earth) along an elliptical path, while another sphere (the moon) is rotating in a circular path around the first sphere. The computations in this paper were performed by using Maple TM. Maple is a trademark of Waterloo Maple Inc. These rotations and the matrices that are yielded are known as orthogonal matrices. Even more specifically they can be thought of as special orthogonal matrices. This thesis investigates the various properties of these rotational matrices along with the relationship between orthogonal matrices and special orthogonal matrices.