The accuracy of the STM is evaluated via RMS error for the unperturbed cases, symplectic check for the gravity perturbed cases and error propagation for the gravity and drag perturbed orbits.
Four types of orbits, LEO, MEO, GTO and HEO, are presented and the simulations are run for 10 orbit periods. Leibniz product rule is used to compute the partials for the recursive formulas and an arbitrary order Taylor series is used to compute the STM.
The method is expanded to include the computation of the STM for the perturbed two-body problem. The method has been proven to be very precise and efficient in trajectory propagation. Analytic Continuation has been developed for the two-body problem based on two scalar variables f and g p and their higher order time derivatives using Leibniz rule. In this work, the Taylor series based technique, Analytic Continuation is implemented to develop a method for the computation of the gravity and drag perturbed State Transition Matrix (STM) incorporating adaptive time steps and expansion order.
