From ntpbooij: Questions are shared in the Mobius Cloud!

+Quaterions_Rotation and +Quaternions_multiplication

The + means question in develop phase.

Dear reader,

Have to create digital questions in Mobius on quaternions. Aim is to teach students of robot engineering about rotations besides the matrix rotations. Made some code, it works but very simplistic. I could not load a (maple) quarternion-toolbox.
Any suggestions?

# quaternion product
# define two vecotrs p and q:
$p0=range(3,3,1);
$px=range(1,1,1);
$py=range(-2,-2,1);
$pz=range(1,1,1);
$q0=range(2,2,1);
$qx=range(-1,-1,1);
$qy=range(2,2,1);
$qz=range(3,3,1);
$p=maple("Vector([$px,$py,$pz])");
$q=maple("Vector([$qx,$qy,$qz])");
$displayp=maple("printf(MathML:-ExportPresentation($p))");
$displayq=maple("printf(MathML:-ExportPresentation($q))");
# p.q=p0.q0-(p.q)+p0.q+q0.p+p*q
# scalar part
$dot=maple("LinearAlgebra[DotProduct]($p,$q,conjugate=false)");
$scalar_part=$p0*$q0-$dot;
# vector part
$cross=maple("LinearAlgebra[CrossProduct]($p,$q)");
$p0q=maple("LinearAlgebra[MatrixMatrixMultiply]($p0,$q)");
$q0p=maple("LinearAlgebra[MatrixMatrixMultiply]($q0,$p)");
$pq=maple("LinearAlgebra[VectorAdd]($p0q,$q0p)");
$vector_part=maple("LinearAlgebra[VectorAdd]($pq,$cross)");
$displayvector_part=maple("printf(MathML:-ExportPresentation($vector_part))");
# unit vectors
$i=maple("Vector([1,0,0])");
$j=maple("Vector([0,1,0])");
$k=maple("Vector([0,0,1])");
# generate answers
$x=maple("LinearAlgebra[DotProduct]($vector_part,$i)");
$y=maple("LinearAlgebra[DotProduct]($vector_part,$j)");
$z=maple("LinearAlgebra[DotProduct]($vector_part,$k)");

###

# rotation using quaternions
# unit vectors
$i=maple("Vector([1,0,0])");
$j=maple("Vector([0,1,0])");
$kk=maple("Vector([0,0,1])");
# rotation axis k:
$kx=range(1,1,1);
$ky=range(1,1,1);
$kz=range(1,1,1);
$k=maple("Vector([$kx,$ky,$kz])");
$displayk=maple("printf(MathML:-ExportPresentation($k))");
# unit vector:
$length=sqrt($kx^2+$ky^2+$kz^2);
$u=maple("LinearAlgebra[Multiply](1/$length,$k)");
$displayu=maple("printf(MathML:-ExportPresentation($u))");
# rotation angle:
$angledeg=range(120,120,1);
$angle=$angledeg*pi/180;
# quaternion:
$scalar=cos($angle/2);
$vector=maple("LinearAlgebra[Multiply](sin($angle/2),$u)");
$displayvector=maple("printf(MathML:-ExportPresentation($vector))");
$qx=maple("LinearAlgebra[DotProduct]($vector,$i)");
$qy=maple("LinearAlgebra[DotProduct]($vector,$j)");
$qz=maple("LinearAlgebra[DotProduct]($vector,$kk)");
# base vector (to be rotated around k)
$bx=range(1,1,1);
$by=range(0,0,1);
$bz=range(0,0,1);
$b=maple("Vector([$bx,$by,$bz])");
$displayb=maple("printf(MathML:-ExportPresentation($b))");
# rotation:
$dot=maple("LinearAlgebra[DotProduct]($u,$b,conjugate=false)");
$cross=maple("LinearAlgebra[CrossProduct]($u,$b)");
$term1=maple("LinearAlgebra[Multiply](cos($angle),$b)");
$displayterm1=maple("printf(MathML:-ExportPresentation($term1))");
$term2=maple("LinearAlgebra[Multiply]((1-cos($angle))*$dot,$u)");
$displayterm2=maple("printf(MathML:-ExportPresentation($term2))");
$term3=maple("LinearAlgebra[Multiply](sin($angle),$cross)");
$displayterm3=maple("printf(MathML:-ExportPresentation($term3))");
$L1=maple("LinearAlgebra[VectorAdd]($term1,$term2)");
$L=maple("LinearAlgebra[VectorAdd]($L1,$term3)");
$displayL=maple("printf(MathML:-ExportPresentation($L))");
# generate answers
$Lx=maple("LinearAlgebra[DotProduct]($L,$i)");
$Ly=maple("LinearAlgebra[DotProduct]($L,$j)");
$Lz=maple("LinearAlgebra[DotProduct]($L,$kk)");

Best regards,

Nico Booij