Rotation Transformations

Many calculations of a roller coaster track require performing a rotation of a specified angle about a specified axis, as shown in figure B.1. It is desirable to know the location of the points in the rotated frame in terms of the unit vectors describing the non-rotated frame. This appendix will illustrate the calculation performed.

Let point be specified in the - coordinate system by the vector .

(B.1) |

From the figure, it can be seen that:

The new position vector, , can now be written as:

The new coordinates can now be written in terms of the non-rotated axes.

(B.2) | |||

(B.3) |