When discussing a Rotation, there are two possible conventions: rotation of the *axes* and rotation of the *object*
relative to fixed axes.

In , let a curve be rotated by a clockwise Angle , so that the original axes of the curve are
and , and the new axes of the curve are and . The Matrix
transforming the original curve to the rotated curve, referred to the original and axes, is

(1) |

(2) |

On the other hand, let the *axes* with respect to which a curve is measured be rotated by a clockwise Angle
, so that the original axes are and , and the new axes are and . Then the Matrix transforming the coordinates of the curve with respect to and is
given by the Matrix Transpose of the above matrix:

(3) |

(4) |

In , rotations of the -, -, and -axes give the matrices

(5) | |||

(6) | |||

(7) |

© 1996-9

1999-05-25