Iterative solution of classical Lambert problem based on analytical gradient

A method based on analytical gradients for solving classical Lambert orbit transfer problem is presented for existing complex solution model and slow convergence rate. The Lambert problem is transformed into transcendental equation for solving the constrained problem with transfer time. The true anomaly is selected as the iterative variable. The analytical gradient of the transfer time with respect to the true anomaly is to update the true anamaly at each iteration step. Theoretical analysis shows that the algorithm has above second-order velocity. The iteration interval is derivedfrom transfer orbit velocity constraints, which deduced from the relationship between eccentricity vector and transfer orbit shape by use of the geometric method, and the iteration initial value of true anomaly is determined by using the linear interpolation algorithm to improve initial guess accuracy. Several simulations have been conducted to demonstrate the validity of the algorithm. The results indicate that the proposed method with high initial guess accuracy improves the convergence rate and converges fast under different transfer conditions. The method can not only converges faster but also has smaller computational complexity compared with the secant iteration algotithm.