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Student[LinearAlgebra]

 RotationMatrix
 construct a rotation Matrix in two or three dimensions

 Calling Sequence RotationMatrix(t, v)

Parameters

 t - rotation angle v - (optional) Vector; axis of the rotation

Description

 • The RotationMatrix(t) command returns the $\mathrm{2x2}$ rotation Matrix corresponding to the angle t, measured in radians.
 • The RotationMatrix(t,v) command returns the $\mathrm{3x3}$ rotation Matrix corresponding to the angle t, where the rotation axis is given by v.  The direction of rotation is determined by using the right-hand rule with respect to v.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > $\mathrm{RotationMatrix}\left(\frac{\mathrm{π}}{4}\right)$
 $\left[\begin{array}{cc}\frac{{1}}{{2}}{}\sqrt{{2}}& {-}\frac{{1}}{{2}}{}\sqrt{{2}}\\ \frac{{1}}{{2}}{}\sqrt{{2}}& \frac{{1}}{{2}}{}\sqrt{{2}}\end{array}\right]$ (1)

Rotation about the y-axis in three-dimensional space:

 > $\mathrm{RotationMatrix}\left(\frac{\mathrm{π}}{3},⟨0,1,0⟩\right)$
 $\left[\begin{array}{ccc}\frac{{1}}{{2}}& {0}& \frac{{1}}{{2}}{}\sqrt{{3}}\\ {0}& {1}& {0}\\ {-}\frac{{1}}{{2}}{}\sqrt{{3}}& {0}& \frac{{1}}{{2}}\end{array}\right]$ (2)

Rotation about an oblique vector in three-dimensional space:

 > $\mathrm{RotationMatrix}\left(1.3,⟨1,1,1⟩\right)$
 $\left[\begin{array}{ccc}{0.5116658857}& {-}{0.3121435208}& {0.8004776350}\\ {0.8004776350}& {0.5116658857}& {-}{0.3121435208}\\ {-}{0.3121435208}& {0.8004776350}& {0.5116658858}\end{array}\right]$ (3)

 See Also