 0410 Celletti, Alessandra, Chierchia, Luigi
 KAM Stability and Celestial Mechanics
(1499K, pdf)
Jan 19, 04

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. KAM theory is a powerful tool apt to prove perpetual stability in
Hamiltonian systems, which are a perturbation of integrable ones. The
smallness requirements for its applicability are well known to be
extremely stringent. A long standing problem, in this context, is the
application of KAM theory to ``physical systems" for ``observable" values
of the perturbation parameters. Here, we consider the Restricted,
Circular, Planar, ThreeBody Problem (RCPTBP),i.e., the problem of
studying the planar motions of a small body subject to the
gravitational attraction of two primary bodies revolving on circular
Keplerian orbits (which are assumed not to be influenced by the small
body). When the mass ratio of the two primary bodies is small the RCPTBP
is described by a nearlyintegrable Hamiltonian system with two degrees of
freedom; in a region of phase space corresponding to nearly elliptical
motions with non small eccentricities, the system is well described by
Delaunay variables. The SunJupiter observed motion is nearly circular
and an asteroid of the Asteroidal belt may be assumed not to influence the
SunJupiter motion. The JupiterSun mass ratio is slightly less than
1/1000. We consider the motion of the asteroid 12 Victoria taking into
account only the SunJupiter gravitational attraction regarding such a
system as a prototype of a RCPTBP. For values of mass ratios up to
1/1000, we prove the existence of twodimensional KAM tori on a fixed
threedimensional energy level corresponding to the observed energy of
the SunJupiterVictoria system. Such tori trap the evolution of phase
points ``close" to the observed physical data of the SunJupiterVictoria
system. As a consequence, in the RCPTBP description, the motion of
Victoria is proven to be forever close to an elliptical motion.
The proof is based on: 1) a new isoenergetic KAM theory; 2) an algorithm
for computing isoenergetic, approximate Lindstedt series; 3) a
computeraided application of 1)+2) to the SunJupiterVictoria system.
 Files:
0410.src(
desc ,
0410.ps )