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Topic: 3d curve formed by cable
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John Owens

Posts: 8
Registered: 12/12/04
3d curve formed by cable
Posted: Jun 17, 1996 5:09 AM
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Our problem is that we wish to simulate graphically the 3d curve formed
by a cable of fixed length whose position, tangent and normal vectors at
both ends are fixed.
A previous correspondance suggested the following:

Let s be the arc length parameter for the curve . Let X(s), T(s), N(s),
and B(s) be the vectors for the position, tangent, normal, and binormal,
resepectively. Let k(s) be the curvature and let t(s) be the torsion.
The two-point boundary value problem is
dX/ds = T X(0), X(L) specified
dT/ds = -kN T(0), T(L) specified
dN/ds = -kT+tB N(0), N(L) sepcified
dB/ds = -tN (though since B = cross(T,N) this last equation is
redundant).

I would appreciate any comments on why the above equations are (or are
not) correct in relation the the physical properties of the cable. I am
also not clear about the mathematical meaning of the curvature and the
torsion.

I would also appreciate any help in solving these equations to give
X(s).

We intend using these equations to model how the curve changes as the
endpoints and tangents and normals are changed, and we can post a flc
file animation of the result to anyone who has an interest once we get
it working.

Thanks in advance for any help,

John Owens

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