6-9 November 2018
DLR Oberpfaffenhofen, Germany
Europe/Amsterdam timezone

Semianalytical Design of Libration Point Formations

8 Nov 2018, 14:00
103 and 105 combined

103 and 105 combined

Building 135
Oral presentation at the conference 12: Verification and Validation Methods Interplanetary Flight and Non-Earth Orbits #3


Dr Sergey Trofimov (Keldysh Institute of Applied Mathematics)


See the pdf file attached.


A novel semianalytical technique is proposed for the libration point formation design. It is based on the use of Lindstedt-Poincare (LP) series that approximate the center manifold in the vicinity of the libration point. Any performance factor can be constructed by symbolically manipulating the LP series. For a number of typical formation-keeping objectives, the optimal design parameters are first obtained analytically in a low-order approximation (n=1,2) and then exploited as an initial guess in the numerical optimization procedure for the 15th-order approximation model. The proposed technique is robust, constructive, and versatile: while avoiding the necessity of numerical integration in the highly unstable dynamical environment, we effectively use the full hierarchy of center manifold approximations. The numerical optimization for the high-order approximation model is still low-dimensional and alleviated by a good initial guess obtained from low-order approximation models.

Primary authors

Dr Sergey Trofimov (Keldysh Institute of Applied Mathematics) Dr Maksim Shirobokov (Keldysh Institute of Applied Mathematics) Mr Michael Koptev (Keldysh Institute of Applied Mathematics)

Presentation Materials

Peer reviewing