Stability Analysis of an Orbiting Plate with Finite Elements

This presentation focuses on rotating equilibria of non-driven systems, which are characterized by the fact that their angular momentum is conserved and non-zero. Sometimes such configurations are called “relative equilibria”. Interesting applications can be found in space dynamics. The stability of relative equilibria of Hamiltonian systems can be analyzed with the “reduced energy momentum method” (REMM) by J. C. Simo, T. A. Posbergh and J. E. Marsden, which has been specialized to systems with cyclic coordinates by the author. The basic idea behind is that the second variation of an “amended potential” must be checked for positive definiteness. For flexible structures relative equilibria can be found with Finite Element software packages. However, in this case the stability analysis is a non-trivial task since one usually has only limited account to the internal data of commercial FE solvers. Therefore, an efficient method will be presented, enabling the application of the REMM as a FE post-processing step where only few data are required from the FE solver, e.g. the equilibrium configuration, the tangent stiffness matrix and the mass matrix. Practical examples from space dynamics will be discussed to demonstrate the method.