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.

MakeRotations[phi,1]

$\left\{\left\{1,0,0\right\},\left\{0,\mathrm{Cos}\left[\mathrm{phi}\right],-\mathrm{Sin}\left[\mathrm{phi}\right]\right\},\left\{0,\mathrm{Sin}\left[\mathrm{phi}\right],\mathrm{Cos}\left[\mathrm{phi}\right]\right\}\right\}$

MakeRotations[{phi,2},{theta,1,1,0}]

$\left\{\left\{\mathrm{Cos}\left[\mathrm{phi}\right]\left(\frac{1}{2}\left(1-\mathrm{Cos}\left[\mathrm{theta}\right]\right)+\mathrm{Cos}\left[\mathrm{theta}\right]\right)-\frac{\mathrm{Sin}\left[\mathrm{phi}\right]\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}},\frac{1}{2}\mathrm{Cos}\left[\mathrm{phi}\right]\left(1-\mathrm{Cos}\left[\mathrm{theta}\right]\right)+\frac{\mathrm{Sin}\left[\mathrm{phi}\right]\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}},\mathrm{Cos}\left[\mathrm{theta}\right]\mathrm{Sin}\left[\mathrm{phi}\right]+\frac{\mathrm{Cos}\left[\mathrm{phi}\right]\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}}\right\},\left\{\frac{1}{2}\left(1-\mathrm{Cos}\left[\mathrm{theta}\right]\right),\frac{1}{2}\left(1-\mathrm{Cos}\left[\mathrm{theta}\right]\right)+\mathrm{Cos}\left[\mathrm{theta}\right],-\frac{\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}}\right\},\left\{-\left(\frac{1}{2}\left(1-\mathrm{Cos}\left[\mathrm{theta}\right]\right)+\mathrm{Cos}\left[\mathrm{theta}\right]\right)\mathrm{Sin}\left[\mathrm{phi}\right]-\frac{\mathrm{Cos}\left[\mathrm{phi}\right]\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}},-\frac{1}{2}\left(1-\mathrm{Cos}\left[\mathrm{theta}\right]\right)\mathrm{Sin}\left[\mathrm{phi}\right]+\frac{\mathrm{Cos}\left[\mathrm{phi}\right]\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}},\mathrm{Cos}\left[\mathrm{phi}\right]\mathrm{Cos}\left[\mathrm{theta}\right]-\frac{\mathrm{Sin}\left[\mathrm{phi}\right]\mathrm{Sin}\left[\mathrm{theta}\right]}{\sqrt{2}}\right\}\right\}$

MakeTranslations