Orbital propagation
around irregular celestial bodies
using the harmonic balance method

Abstract

This thesis presents a frequency-domain framework for the computation and analysis of periodic and quasi-periodic orbits in astrodynamics. The harmonic balance method is adapted to autonomous and conservative systems to compute periodic solutions efficiently while providing direct access to their stability and bifurcations. The method’s performance is first validated on a benchmark two degrees of freedom system and then applied to the circular restricted three-body problem, where it reproduces classical families of periodic orbits and reveals new connections between resonant branches through bifurcation analysis. The approach is then extended to the gravitational environment of asteroid 433 Eros, modeled using the polyhedron method. A dense map of periodic families, comprising over one hundred bifurcations, is established, offering new insights into the resonance structure and transitions between orbital modes. The multi-harmonic balance method is further introduced to compute quasi-periodic orbits, enabling the study of multi-frequency dynamics directly in the frequency domain. Finally, the method is extended to more realistic scenarios by incorporating solar radiation pressure and binary gravitational effects, demonstrated through the Didymos–Dimorphos system. The results confirm that the harmonic balance framework provides a powerful, efficient, and insightful alternative to classical time-domain techniques for orbital propagation around irregular celestial bodies.

Jury members  

•  L. SALLES, Université de Liège, Président;
• G. KERSCHEN, Université de Liège, Promoteur;
• G. RAUW, Université de Liège;
• G. RAZE, Université de Liège;
• L. DELL’ELCE, INRIA (France);
• J. DAQUIN, Université de Toulon (France).

Retransmission also available on  the PhD channel