Singularities in Dromo formulation. Analysis of deep flybys

Abstract

The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very specific situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric flybys. The performance of Dromo is evaluated in different scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical flybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the flyby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity.

Kustaanheimo–Stiefel Variables for Planetary Protection Compliance Analysis

“…Recent revisions worked to fix these sensitivity issues: Baù et al [33] developed E-DROMO, a non-singular formulation of DROMO for any bound orbit, removing the singularities on null eccentricity and inclination. Roa et al [34] analyzed the singularities posed by deep flybys and then proposed the re-formulation H-DROMO, not sensitive to a vanishing angular momentum. The latest updates involve the study of the evolution of an intermediate frame [35].…”

Advanced orbit propagation methods applied to asteroids and space debris

“…However, it is important to stress that only K-S and Stiefel-Scheifele's elements can deal with collision orbits (i.e., with vanishing angular momentum), and so avoid both topological and physical singularities. The singularity for vanishing angular momentum was characterized in detail in [86] for the Dromo formulation, who proposed possible solutions to mitigate this issue.…”