Lambert’s problem and solution by non-rational Bézier functions:

Solving Lambert’s problem is one of the fundamental problems in astrodynamics. In this paper, it is first shown in a systematic fashion how Lambert’s problem can be expressed as a univariate equation of one of the orbital elements or various variables related to the orbital elements. Some of the choices of independent variables reported in the literature in formulating Lambert’s problem are shown to be special cases of such more general treatment, in a clear and logical fashion. This development produces a new formulation of Lambert’s problem in terms of the argument of periapsis. A new efficient algorithm using non-rational Bezier functions is designed to solve Lambert’s problem, which takes full advantage of the monotonicity and boundedness of the argument of periapsis as the independent variable and no initial guess is required for this new algorithm. Numerical comparison results are provided to demonstrate the effectiveness and efficiency of the algorithm.