Lambert’s problem involves solving the orbits connecting two position vectors with a given flight time. When introducing variations to the input of this problem (that is, terminal positions and the flight time), the output terminal velocities vary in response. The higher-order Lambert problem pursues a higher-order Taylor approximation of the output with respect to the input. Instead of finding a real number root, Householder methods are adapted to find a Taylor series solution of the transfer-time equation. By using explicit derivatives of the transfer-time equation, the newly implemented Householder methods converge faster than the general partial inversion method. In applications such as pork-chop plots and orbital admittance maps that require solving a large number of Lambert’s problems, a higher-order Lambert solution can reduce the running time by more than 80% when compared to solving the original Lambert problems one by one. Furthermore, the investigation of the parameter space of Lambert’s problem yields useful insights to the selection of higher-order expansion points.


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    Title :

    Higher-Order Lambert Problem Solution Based on Differential Algebra


    Contributors:
    Shu, Peng (author) / Yang, Zhen (author) / Luo, Ya-Zhong (author)

    Published in:

    Publication date :

    2022-10-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English





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