MakeRotations(erms)

MakeRotations([erms1], ..., [ermsn])

MakeRotations(rm)

erms,erms1, ..., ermsn: elementary rotation-matrix specifications

rm: rotation matrix

The function MakeRotations returns a rotation matrix as specified by its arguments.

An elementary rotation-matrix specification comes in one of two forms, namely

phi,i

where phi is an algebraic expression and i equals 1, 2, or 3. This corresponds to a rotation by an angle phi about the i-th basis vector.

phi,v1,v2,v3

where phi, v1, v2, and v3 are algebraic expressions. This corresponds to a rotation by an angle phi about the vector whose coordinates equal v1, v2, and v3.

When invoked with multiple elementary rotation-matrix specifications, the MakeRotations procedure returns the matrix product of the individual rotation matrices specified by each of the elementary rotation-matrix specifications.

$\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left(\mathrm{phi}\right)& -\sin \left(\mathrm{phi}\right)\\ 0& \sin \left(\mathrm{phi}\right)& \cos \left(\mathrm{phi}\right)\end{array}\right]$

$\left[\begin{array}{ccc}\cos \left(\mathrm{phi}\right)\left(\frac{1}{2}\cos \left(\mathrm{theta}\right)+\frac{1}{2}\right)-\frac{1}{2}\sin \left(\mathrm{phi}\right)\sin \left(\mathrm{theta}\right)\sqrt{2}& \cos \left(\mathrm{phi}\right)\left(\frac{1}{2}-\frac{1}{2}\cos \left(\mathrm{theta}\right)\right)+\frac{1}{2}\sin \left(\mathrm{phi}\right)\sin \left(\mathrm{theta}\right)\sqrt{2}& \frac{1}{2}\cos \left(\mathrm{phi}\right)\sin \left(\mathrm{theta}\right)\sqrt{2}+\sin \left(\mathrm{phi}\right)\cos \left(\mathrm{theta}\right)\\ \frac{1}{2}-\frac{1}{2}\cos \left(\mathrm{theta}\right)& \frac{1}{2}\cos \left(\mathrm{theta}\right)+\frac{1}{2}& -\frac{1}{2}\sin \left(\mathrm{theta}\right)\sqrt{2}\\ -\sin \left(\mathrm{phi}\right)\left(\frac{1}{2}\cos \left(\mathrm{theta}\right)+\frac{1}{2}\right)-\frac{1}{2}\cos \left(\mathrm{phi}\right)\sin \left(\mathrm{theta}\right)\sqrt{2}& -\sin \left(\mathrm{phi}\right)\left(\frac{1}{2}-\frac{1}{2}\cos \left(\mathrm{theta}\right)\right)+\frac{1}{2}\cos \left(\mathrm{phi}\right)\sin \left(\mathrm{theta}\right)\sqrt{2}& -\frac{1}{2}\sin \left(\mathrm{phi}\right)\sin \left(\mathrm{theta}\right)\sqrt{2}+\cos \left(\mathrm{phi}\right)\cos \left(\mathrm{theta}\right)\end{array}\right]$

MakeTranslations