New lambert algorithm using the Hamilton-Jacobi-Bellman equation

A study was conducted to demonstrate the formulation of the new Lambert Algorithm using the Hamilton-Jacobi-Bellman Equation (HJB). The two-point boundary-value problem (TPBVP) of the Hamiltonian system was treated as an optimal control problem where the Lagrangian function played a role as a performance index. The approach demonstrated in the study was based on the expansion of the value function in the Chebyshev series with unknown coefficients, considering the computational advantages of the use of Chebyshev polynomials. The differential expressions that arose in the HJB equation were expanded in Chebyshev series with the unknown coefficients. The new algorithm had the potential to provide a solution to the TPVBP using the spectral information about the gravitation potential function and was applicable to the problem under a higher-order perturbed potential function without any modification.