MARTIN W. LO
Jet Propulsion Laboratory
Pasadena, California
mwl@trantor.jpl.nasa.gov
Abstract:
The importance of invariant manifolds in dynamical systems theory is well
known ever since Poincare's
work on celestial mechanics. In particular, Poincare identified
heteroclinic and homoclinic cycles as key
features of a dynamical system from which chaotic motion can arise. The
Genesis Mission uses the
heteroclinic behavior between the L1 and L2 Sun-Earth Lagrange points to
collect and return solar wind
samples to the Earth (launch in 1/7/2000, Lo et al). The motions of comets
also follow the
heteroclinic/homoclinic cycles of the Sun-Jupiter L1 and L2 Lagrange points
(Lo and Ross). These results
led to the numerical computation of heteroclinic/homoclinic cycles between
Lyapunov orbits around L1
and L2 (Koon et al [1999]). By coupling three-body systems (e.g.
Jupiter-Ganymede, Jupiter-Europa) a
new mission concept was produced, the Petit Grand Tour of Jovian or
Saturnian satellites (Koon et al
[1999, Aug. 1999]). Refinements of these techniques combined with
understanding of the satellite capture
mechanism recently enabled the solution of a long standing problem, a
dynamical explanation of and a
systematic algorithm for the ballistic transfer and capture of spacecraft
to the Moon. Additional work on
modeling the Temporary Capture of Jupiter comets using 3-dimensional halo
orbits have also yielded
excellent matches between pieces of the invariant manifolds of halo orbits
with comet orbits in the Jupiter
region (Howell et al). Many new problems and applications are suggested by
these results. In particular, the
use of dynamical systems theory in optimal control problems may supply
powerful new tools for space
mission design as well as other applications (Serban et al, see Linda
Petzold's talk). NASA/JPL has
embarked on the development of a next-generation mission design tool using
dynamical systems theory,
LTool. Some interesting features of this tool, currently under
implementation, will be described.
References
Lo, Martin et al, [1998] Genesis Mission Design, Paper No. AIAA 98-4468, to
appear in J. of Astronautical
Sciences
Lo, Martin, S. Ross [1997] SURFing the Solar System: Invariant Manifolds and the Dynamics of the Solar System, JPL IOM 312/97
Koon, W.S., M. Lo, J. Marsden, S. Ross [1999] Heteroclinic Connections between Periodic Orbits and Resonance Transitions in Celestial Mechanics, to appear in Chaos
Koon, W.S., M. Lo, J. Marsden, S. Ross [August 1999] Heteroclinic Connections and the Genesis Trajectory, Paper No. AAS 99-451
Howell, K., B. Marchand, M. Lo, S. Ross [1999] Temporary Satellite Capture of Short-Period Jupiter Family Comets from the Perspective of Dynamical Systems, abstract
Serban, R., L. Petzold, W.S. Koon, M. Lo, J. Marsden, L. Petzold, S. Ross, R. Wilson [1999] Genesis Mission Correction Maneuvers Using Optimal Control, draft