Lambert’s two-body orbital boundary value problem (BVP) is the determination of the terminal velocity vectors of a trajectory connecting two fixed positions in a specified transfer time. The solution to Lambert’s problem is often the basis for preliminary trajectory design and optimization. In this work, several related two-body orbital BVPs, with constraints involving terminal velocities, flight-path angle, Δv, final radius, transfer angle, etc., are studied. Exact solutions to these BVPs are derived in a universal form via the Kustaanheimo-Stiefel transformation. The solutions are regular and completely analytic if the energy of the transfer orbit is known a priori. Otherwise, they require root-finding of either a polynomial or a transcendental equation with well-defined bounds on its roots. The algorithms developed are validated on several orbit transfer problems and can enable complex mission analysis and parametric studies or serve as initial guesses for high-fidelity numerical optimization schemes.


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    Title :

    Two-Body Orbital Boundary Value Problems in Regularized Coordinates


    Additional title:

    J Astronaut Sci


    Contributors:

    Published in:

    Publication date :

    2020-06-01


    Size :

    40 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




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