An effective method for the design of fuel-optimal transfers in two-and threebody dynamics is presented. The optimal control problem is formulated using calculus of variation and primer vector theory. This leads to a multi-point boundary value problem (MPBVP), characterized by complex inner constraints and a discontinuous thrust profile. The first issue is addressed by embedding the MPBVP in a parametric optimization problem, thus allowing a simplification of the set of transversality constraints. The second problem is solved by representing the discontinuous control function by a smooth function depending on a continuation parameter. The resulting trajectory optimization method can deal with different intermediate conditions, and no a priori knowledge of the control structure is required. Test cases in both the two-and three-body dynamics show the capability of the method in solving complex trajectory design problems.
The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits.In this paper, the geometrical and dynamical properties of the Sun-Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on L 1,2 Lagrange point orbits. Sun-Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.
In this paper, two numerical methods for nonlinear uncertainty propagation in astrodynamics are presented and thoroughly compared. Both methods are based on the Monte Carlo idea of evaluating multiple samples of an initial statistical distribution around the nominal state. However, whereas the graphics processing unit implementation aims at increasing the performances of the classical Monte Carlo approach exploiting the massively parallel architecture of modern general-purpose computing on graphics processing units, the method based on differential algebra is aimed at the improvement and generalization of standard linear methods for uncertainty propagation. The two proposed numerical methods are applied to test cases considering both simple two-body dynamics and a full nn-body dynamics with accurate ephemeris. The results of the propagation are thoroughly compared with particular emphasis on both accuracy and computational performances
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