Algorithm 667: Sigma—a stochastic-integration global minimization algorithm
ACM Transactions on Mathematical Software (TOMS)
Removing the stiffness of curvature in computing 3-D filaments
Journal of Computational Physics
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
A symbolic-numeric approach to tube modeling in CAD systems
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
| Hi-index | 0.00 |
We study solution methods for boundary value problems associated with the static Kirchhoff rod equations. Using the well known Kirchhoff kinetic analogy between the equations describing the spinning top in a gravity field and spatial rods, the static Kirchhoff rod equations can be fully integrated. We first give an explicit form of a general solution of the static Kirchhoff equations in parametric form that is easy to use. Then by combining the explicit solution with a minimization scheme, we develop a unified method to match the parameters and integration constants needed by the explicit solutions and given boundary conditions. The method presented in the paper can be adapted to a variety of boundary conditions. We detail our method on two commonly used boundary conditions.