Abstract
This paper presents the optimal control approach to solve both Lambert’s problem and Gibbs’ method, which are commonly used for preliminary orbit determination. Lambert’s problem is reinterpreted with Hamilton’s principle and is converted to an optimal control problem. Various extended Lambert’s problems are formulated by modifying the weighting and constraint settings within the optimal control framework. Furthermore, Gibbs’ method is also converted to an extended Lambert’s problem with two position vectors and one orbit energy with the help of the proposed orbital energy computation algorithm. The proposed extended Lambert’s problem and Gibbs’ method are numerically solved with the Lobatto pseudospectral method, and their accuracies are verified by numerical simulations.
Highlights
Lambert’s problem and Gibbs’ method are both preliminary orbit determination methods.Lambert’s problem is a two-point boundary value problem (TPBVP) that finds the trajectory in a two-body orbit with two position vectors at a given time of flight
The proposed extended Lambert’s problem and Gibbs’ method are numerically solved with the Lobatto pseudospectral method, and their accuracies are verified by numerical simulations
Gibbs’ method calculates the velocity of the middle position using three position vectors given at three successive times
Summary
Lambert’s problem and Gibbs’ method are both preliminary orbit determination methods. One is the optimal control formulation of Gibbs’ method for orbit determination and the other is the Lambert’s problem under J2 perturbation. Gibbs’ method is converted to an extended Lambert’s problem using two position vectors and one orbital energy as boundary conditions; Appl. Gibbs’ method is solved along with the proposed orbital energy computation algorithm. A new approach to solving Lambert’s problem under J2 perturbation is presented by modifying the potential energy term in our optimal control framework. This paper is organized as follows: in Section 2, Lambert’s problem is explained and it is shown that it can be formulated as an optimal control problem; in Section 3, various extended Lambert’s problems are presented using different weighting, constraint, and potential energy settings within the optimal control framework; Section 4 proposes an alternative Gibbs’ solution using an extended.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
