Modified Picard Integrator for Spaceflight Mechanics

This paper investigates the applicability of the Parker–Sochacki Picard iteration method for spaceflight mechanics. Notably, solving initial value problems, parallel integration of multiple trajectories, and high-order state transition tensor computations are addressed. This paper presents a systematic approach to transforming vector fields to polynomial form, which is required for the method investigated. The application of this approach is presented on a few vector fields, including spherical harmonics gravity field. The initial cost of transforming the vector field can be justified by the performance of the initial value problem solver. Additionally, this polynomial form of the vector field is used in the calculation of state transition tensors with differentiation of polynomials only. This reduces the computations required to obtain state transition tensors for some problems and is discussed in this paper. An efficient representation of vector fields in polynomial form benefits the implementation of t...

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