Orbital propagation around irregular celestial bodies using the harmonic balance method

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.