Analytical solution to the form-finding problem for tensegrities using the all minors theorem in algebra

Source abstract

A procedure to obtain an equilibrium configuration of tensegrities is presented. The method proposed is based on a well-known theorem of algebra which allows the coefficients in the characteristic polynomial of a matrix to be obtained as the sum of the principal minors. The primary advantage of the procedure proposed lies in the simplicity of its implementation and the fact that it can provide an analytical solution to the form-finding problem for large tensegrity structures. This procedure is particularly valuable since the high computational cost of obtaining the different analytical solutions, rather than a single numerical one, would otherwise be infeasible. The methodology is especially beneficial for tensegrity structures derived from specific topological patterns, where the inherent repetitiveness of topological connectivity can significantly reduce the number of minors that need to be computed.