Controlling chaos

http://www.dept.aoe.vt.edu/~cdhall/courses/KlueverText/SDC.pdf

Spacecraft Dynamics and Control

This paper concerns heteroclinic connections and resonance transitions in the planar circular
restricted 3-body problem, with applications to the dynamics of comets and asteroids and the design
of space missions such as the Genesis Discovery Mission and low energy Earth to Moon transfers.
The existence of a heteroclinic connection between pairs of equal energy periodic orbits around two of
the libration points is shown numerically. This is applied to resonance transition and the construction
of orbits with prescribed itineraries. Invariant manifold structures are relevant for transport between
the interior and exterior Hill’s regions, and other resonant phenomena throughout the solar system.

/pdf/dynamical-systems-the-three-body-problem-and-space-mission-48b7chyrqv.pdf

Dynamical Systems, the Three-Body Problem and Space Mission Design

This paper offers a modification of the Cowell method for the integration of orbits The modification is characterized by the property that it will integrate unperturbed Kepler motion exactly (excluding truncation errors), thus the slight instability of the Cowell Method is avoided Furthermore, the modification takes into account the most important secular effects of orbit motion As an example of the applicability of the modified method to perturbed motion, the equations of motion of an artificial earth satellite are integrated In the case of elliptic initial conditions regularization by a Levi-Civita transformation was used

Stabilization of Cowell's method

In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less ΔV than a standard Hohmann transfer. In this paper, we apply the dynamical systems techniques developed in our earlier work to reproduce systematically a Hiten-like mission. We approximate the Sun—Earth—Moon-spacecraft 4-body system as two 3-body systems. Using the invariant manifold structures of the Lagrange points of the 3-body systems, we are able to construct low energy transfer trajectories from the Earth which execute ballistic capture at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations.

/pdf/low-energy-transfer-to-the-moon-3uffvfo4br.pdf

E. Grebenikov

Papers

Theory of Orbits-The Restricted Problem of Three Bodies.