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Simplified existence and uniqueness conditions for the zeros and the concavity of the F and G functions of improved Gauss orbit determination from two position vectors

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  • Danchick, Roy

Abstract

In our first paper we showed how Gauss's method for determining the initial position and velocity vectors from two inertial position vectors at two times in an idealized Keplerian two-body elliptical orbit can be made more robust and efficient by replacing functional iteration with Newton–Raphson iteration. To do this we split the orbit determination algorithm into two sub-algorithms, the x-iteration to find the zero of the fixed-point function F(x) when the true anomaly angular difference between the two vectors is large and the y-iteration to find the zero of the fixed-point function G(y) when the angular difference is small.

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  • Danchick, Roy, 2015. "Simplified existence and uniqueness conditions for the zeros and the concavity of the F and G functions of improved Gauss orbit determination from two position vectors," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 279-287.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:279-287
    DOI: 10.1016/j.amc.2015.07.008
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    References listed on IDEAS

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    1. Andreu, Carlos & Cambil, Noelia & Cordero, Alicia & Torregrosa, Juan R., 2014. "A class of optimal eighth-order derivative-free methods for solving the Danchick–Gauss problem," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 237-246.
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