High levels of space debris, created by decades of human activity in space, are becoming an increasing threat to astronauts and satellites alike. To tackle this issue, innovative solutions for cleaning space are called for. One company with a promising concept is Clearspace, who propose the use of satellites with claw-like arms that can be used to catch and de-orbit large pieces of debris. Designing such a satellite is highly complex and requires large financial means. To reduce the dependency on expensive testing during the development phase, simulations can be used as a cheap option for fast prototyping and analysis of ideas. However, conventional simulation tools can be very slow and thus delay or even hinder the creative process. Thus, a new simulation tool is called for that can quickly and efficiently simulate the behaviour of structures in large rotation and translation over long periods of time. This report presents the theory and results of the WOBBLE code package that has been developed by the authors of this report as a means to provide such efficient simulation capabilities. The package is a supplement to the finite element code Akantu [1] and thus builds on the work of the EPFL LSMS1. WOBBLE is an acronym for Waves Of Beams and other Bodies due to Loadings and Excitations and has been chosen because the package is based on a combination of modal analysis and rigid body mechanics. The first two sections of this report present the theory of modal analysis and rigid body motion, which form the theoretical basis of the simulation code. Next, Section 4 discusses how the implemented models can be used for efficient simulations. Section 5 then presents the verification of the WOBBLE simulation results using analytical models and the existing Akantu code. A comparative case study for a more realistic pulse forcing is presented in Section 6. Finally, recommendations for future work are given in Section 7 and the report is concluded in Section 8. Additional information on the practical usage of the WOBBLE code can be found in Appendix A.