# This stuff at the top is just documentation; cut and paste the stuff
# below the #s into Maple.
#
# Briefly:
#
# rv(x(t),y(t),z(t),a,b,c,thick) draws the parametric curve
# r(t)=(x(t),y(t),z(t)) for a<=t<=b, and at the point t=c, draws the
# velocity vector r'(c).
#
# rva(x(t),y(t),z(t),a,b,c,thick) draws the parametric curve
# r(t)=(x(t),y(t),z(t)) for a<=t<=b, and at the point t=c, draws the
# velocity vector r'(c) and the acceleration vector a'(c).
#

with(plots):
rv := proc (x,y,z,a,b,c,thick)
   local r,rplot,v,vplot;
   r := [x,y,z];
   rplot := tubeplot(r,t=a..b,radius=thick,axes=normal);
   v := [diff(x,t),diff(y,t),diff(z,t)];
   vplot := arrow(eval(r,t=c),eval(v,t=c),width=thick,color=red);
   display3d({rplot,vplot});
end proc:
rva := proc (x,y,z,a,b,c,thick)
   local r,rplot,v,vplot,acc,accplot;
   r := [x,y,z];
   rplot := tubeplot(r,t=a..b,radius=thick,axes=normal);
   v := [diff(x,t),diff(y,t),diff(z,t)];
   vplot := arrow(eval(r,t=c),eval(v,t=c),width=thick,color=red);
   acc := [diff(v[1],t),diff(v[2],t),diff(v[3],t)];
   accplot := arrow(eval(r,t=c),eval(acc,t=c),width=thick,color=blue);
   display3d({rplot,vplot,accplot});
end proc:

tubeplot([cos(t),sin(t),-t],t=-Pi..2*Pi,radius=0.1,axes=normal);
rv(cos(t),sin(t),t,0,2*Pi,3*Pi/2,0.05);
rva(cos(t),sin(t),t,0,2*Pi,3*Pi/2,0.05);