The first-order,non-singular Keplerian differential state transition matrix |
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| Authors: | Stefano Casotto |
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| Institution: | 1.Dipartimento di Fisica e Astronomia,Università di Padova,Padua,Italy |
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| Abstract: | The Keplerian differential state transition matrix (KDSTM) is a fundamental tool in investigations of the sensitivity of orbital evolution to changes in initial conditions, in perturbation analysis, as well as in targeting and rendezvous operations. Several different forms of the KDSTM are available in the literature. They differ in the choice of state space variables, as well as in derivation methods. Here, a new method for constructing the KDSTM is presented, which is based on the well-known theorem on the differentiability of the solution of a system of ordinary differential equations with respect to initial conditions. A peculiarity of the method is that it allows the direct construction of analytical expressions for both the direct and the inverse fundamental matrices needed to form the KDSTM. The KDSTM is first built in the inertial reference frame and then transformed to the orbital, or Hill reference frame. The resulting expressions contain the full set of Keplerian elements and are hence readily extensible to perturbed Keplerian reference motion. The results are compared with some of the best known KDSTM’s available in the literature, with which they are proven to be fully equivalent, despite their sometimes dramatically different appearance. |
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