To illustrate the significance of using initial conditions that satisfy the configuration constraints.

This Mambo project contains a non-stationary blocks. The non-stationary block may be positioned and oriented relative to the world observer in two independent steps, namely

1. Specify the location of a reference point B on the block.
2. Specify a position of the point B.
3. Specify an orientation of the block about the point B.

The motion of the block is constrained in such a way that the point B is stationary.

lx, ly, and lz: lengths of the sides of the blocks.

Bx, By, and Bz: coordinates of the point B in a coordinates system with origin at the center of the block and axes parallel to the edges of the block.

marker: radius of a sphere at the point B.

q1, q2, and q3: coordinates of the point B in a coordinate system with origin at the reference point of the world observer and axes parallel to the basis vectors of the reference triad of the world observer.

q4, q5, and q6: 3-1-3 sequence of Euler angles representing the orientation of the block relative to the reference triad of the world observer.

Modify the Mambo project so as to constrain the point B to move with constant velocity along a circular/ellipsoidal/helical path relative to the world observer.

topoint.zip (zip file, 12 kb, December 30, 2012)
This zip archive contains MAMBO and the MAMBO toolbox source files to visualize the MAMBO project and regenerate visualization files using maple 16, mupad 5.6.0 (matlab R2011a), and mathematica 8.0 versions of the code found below.

>Restart():

>DeclareObservers(W,B):
>DeclarePoints(W,B,BlockCenter,seq(seq(cat(E,i,j),i=1..3),j=1..4)):
>DeclareTriads(w,b):
>DefineObservers([W,W,w],[B,B,b]):
>DefinePoints([W,B,w,q1,q2,q3],[B,BlockCenter,b,Bx,By,Bz],[BlockCenter,E11,b,0,ly/2,lz/2],[BlockCenter,E12,b,0,ly/2,-lz/2],[BlockCenter,E13,b,0,-ly/2,-lz/2],[BlockCenter,E14,b,0,-ly/2,lz/2],[BlockCenter,E21,b,lx/2,0,lz/2],[BlockCenter,E22,b,lx/2,0,-lz/2],[BlockCenter,E23,b,-lx/2,0,-lz/2],[BlockCenter,E24,b,-lx/2,0,lz/2],[BlockCenter,E31,b,lx/2,ly/2,0],[BlockCenter,E32,b,lx/2,-ly/2,0],[BlockCenter,E33,b,-lx/2,-ly/2,0],[BlockCenter,E34,b,-lx/2,ly/2,0]):
>DefineTriads(w,b,[q4,3],[q5,1],[q6,3]):
>DefineNeighbors([W,B]):

>DefineObjects(
   seq([B,'Block',point=cat(E,1,j),xlength=lx,ylength=(lx+ly+lz)/30,zlength=(lx+ly+lz)/30,color=yellow],j=1..4),
   seq([B,'Block',point=cat(E,2,j),xlength=(lx+ly+lz)/30,ylength=ly,zlength=(lx+ly+lz)/30,color=yellow],j=1..4),
   seq([B,'Block',point=cat(E,3,j),xlength=(lx+ly+lz)/30,ylength=(lx+ly+lz)/30,zlength=lz,color=yellow],j=1..4),
   [B,'Sphere',radius=marker,color=red]):

>DeclareStates(q1,q2,q3,q4,q5,q6):
>linvel:=LinearVelocity(W,B):
>angvel:=AngularVelocity(w,b):
>kde:={seq(angvel &oo MakeTranslations(b,i) = cat(u,i+3),i=1..3),seq(linvel &oo MakeTranslations(w,i) - off*cat(u,i)=0,i=1..3)}:

>GeometryOutput(main=W,states=[q1,q2,q3,q4,q5,q6],parameters=[Bx,By,Bz,lx,ly,lz,marker],checkargs,checktree,filename="topoint.geo"):
>MotionOutput(ode=kde,states=[q1,q2,q3,q4=2,q5=2.2,q6=1.5],parameters=[lx=.25,ly=.5,lz=1,Bx=0.125,By=.25,Bz=.5,marker=.1],insignals=[u1=-cos(2*t),u2=-cos(t),u3=sin(t),u4=cos(2*t),u5=0.1,u6=sin(t),off=(sin(t)&>=0)],checkargs,checksings,filename="topoint.dyn");