Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

The halo orbits around the Earth-Moon L2 libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recentl...

Error Analysis for Picard-Chebyshev Iterations

The Chebyshev iteration revisited

Compared to Krylov space methods based on orthogonal or oblique projection, the Chebyshev iteration does not require inner products and is therefore particularly suited for massively parallel computers with high communication cost. Here, six different algorithms that implement this method are presented and compared with respect to roundoff effects, in particular, the ultimately achievable accur...

A Picard Iteration Based Integrator

converge to a unique solution of the IVP up to the boundary of U [1]. In general, φn may converge slowly to the exact solution. The Picard iteration based integrator described in this paper has three main advantages. The the integrator has arbitrary order, is time adaptive, and has dense output. Dense output refers to the integrator being able to take time steps of variable length without havin...

Stability of halo orbits.

We predict new populations of trapped nonequatorial ("halo") orbits of charged dust grains about an arbitrary axisymmetric planet. Simple equilibrium and stability conditions are derived, revealing dramatic differences between positively and negatively charged grains in prograde or retrograde orbits. Implications for the Cassini mission to Saturn are discussed.