EDromo

The EDromo state vector is a non-singular set of 8 orbital elements designed for accurate trajectory propagation, especially in the presence of perturbations. It combines aspects of equinoctial and quaternion elements to avoid singularities associated with near-circular or near-equatorial orbits. It's benefits come from the regularization techniques to make the propagation of the set exceptionally numerically stable.

Components

The EDromo state vector [ζ₁, ζ₂, ζ₃, ζ₄, ζ₅, ζ₆, ζ₇, ζ₈] consists of eight elements:

• In-Plane Elements

  • ζ₁: In-plane element related to eccentricity and argument of periapsis.
  • ζ₂: In-plane element related to eccentricity and argument of periapsis.
  • ζ₃: Corresponds to orbital energy.

• Quaternion Elements (Orientation)

  • ζ₄: Quaternion element 1.
  • ζ₅: Quaternion element 2.
  • ζ₆: Quaternion element 3.
  • ζ₇: Quaternion element 4.

• Time Element

  • ζ₈: Time element, which can represent physical, constant, or linear time.

Special Configurations

Unlike other coordinate systems, the transformation to and from EDromo coordinates requires a set of special configuration parameters. These are necessary for non-dimensionalization and for defining the fictitious time frame.

A helper function is provided to generate these parameters from a standard Cartesian state.

References

[1]: Baù, G., Bombardelli, C., Peláez, J., and Lorenzini, E., "Nonsingular orbital elements for special perturbations in the two-body problem". MNRAS 454(3), pp. 2890-2908. 2015. [2]: Amato, Davide. "THALASSA: Orbit propagator for near-Earth and cislunar space." Astrophysics Source Code Library (2019): ascl-1905.