The Multi-Stage-Lambert Scheme for steering a satellite-launch vehicle (SLV)

The determination of an orbit, having a specified transfer time (time-of-flight) and connecting two position vectors, frequently referred to as the Lambert problem, is fundamental in astrodynamics. Of the many techniques existing for solving this two-body, two-point, time-constrained orbital boundary-value problem, Gauss´ and Lagrange´s methods were combined to obtain an elegant algorithm based on Battin´s work. This algorithm included detection of cross-range error. A variable TYPE, introduced in the transfer-time equation, was flipped, to generate the inverse-Lambert scheme. In this paper, an innovative adaptive scheme is presented, which is called ldquothe multi-stage-Lambert schemerdquo. This scheme proposes a design of autopilot, which achieves the predecided destination position and velocity vectors for a multi-stage rocket, when each stage is detached from the main vehicle after it burns out, completely.