K/S Lambert problem

The Lambert problem in orbital mechanics is formulated in Kustaanheimo/Stiefel variables. The problem is to determine the required energy and the value of the generalized eccentric anomaly such that a particle at the initial position vector will transfer to the final position vector in a physical time interval. The fictitious time solution results in two nonlinear equations in the two unknowns, energy and fictitious time. The generalized eccentric anomaly solution, however, results in only one nonlinear equation in the one unknown, the eccentric anomaly. This simplification is possible because the energy equation is separable in the eccentric anomaly formulation.