Derivative analysis and algorithm modification of transverse-eccentricity- based lambert problem

The classical Lambert problem can be parameterized and solved through the transverse-eccentricity component.A further study is conducted to calculate the analytical derivative of the transverse-eccentricity-based Lambert problem and to modify its algorithm. Results show that the derivative of the direct Lambert problem is positive and continuous, verifying that the transfer time monotonically increases with the transverse eccentricity. However, the derivative of the multirevolution Lambert problem increases from negative to positive, indicating that the transfer time initially decreases to the minimum value and then increases to infinity. The original solution algorithm is improved by introducing the analytical derivative. Numerical simulations for different cases show that, compared with the two existing transverse- eccentricity-based methods, the average computational time cost decreases by 65.5 and 39.8%, respectively.