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.
Two-Body Orbital Boundary Value Problems in Regularized Coordinates
J Astronaut Sci
The Journal of the Astronautical Sciences ; 67 , 2 ; 387-426
01.06.2020
40 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Lambert’s problem , Trajectory design , Kustaanheimo-Stiefel transformation , Orbital boundary value problems Engineering , Aerospace Technology and Astronautics , Mathematical Applications in the Physical Sciences , Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)
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