High-Accuracy Orbital Dynamics Simulation through Keplerian and Equinoctial Parameters

In the last few years a Modelica library for spacecraft modelling and simulation has been developed, on the basis of the Modelica Multibody Library. The aim of this paper is to demonstrate improvements in terms of simulation accuracy and efficiency which can be obtained by using Keplerian or Equinoctial parameters instead of Cartesian coordinates as state variables in the spacecraft model. The rigid body model of the standard MultiBody library is extended by adding the equations defining a transformation of the body center-of-mass coodinates from Keplerian and Equinoctial parameters to Cartesian coordinates, and by setting the former as preferred states, instead of the latter. The remaining parts of the model, including the model of the gravitational field, are left untouched, thus ensuring maximum re-usability of third-party code. The results shown in the paper demonstrate the superior accuracy and speed of computation in the reference case of a point-mass gravity field.