Numerical Analysis of Invariant Manifolds Characterized by Quasi-Periodic Oscillations of Nonlinear Systems

Quasi-periodic motions systematically occur, when a system is subjected to multiple unrelated excitation mechanisms. Since unrelated mechanisms generically exhibit independent frequencies, the resulting motion is characterized by multiple fundamental frequencies. Consequently, the resulting motion is not periodic, but, due to the independent frequencies, sort of periodic, namely quasi-periodic. Not being able to identify one unique fundamental frequency, established methods for the identification of periodic motions are impracticable. In order to calculate and analyze a quasi-periodic motion, approaches to the invariant toroidal manifold, which is the hull of a quasi-periodic motion, are utilized. This thesis provides the theoretical frameworks for the developed analyzing program Quont, which is capable of calculating, analyzing and continuing quasi-periodic motions of arbitrary dynamical systems.