56 research outputs found
The role of chaotic resonances in the solar system
Our understanding of the Solar System has been revolutionized over the past
decade by the finding that the orbits of the planets are inherently chaotic. In
extreme cases, chaotic motions can change the relative positions of the planets
around stars, and even eject a planet from a system. Moreover, the spin axis of
a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with
adverse effects on the climates of otherwise biologically interesting planets.
Some of the recently discovered extrasolar planetary systems contain multiple
planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure
Relativistic Celestial Mechanics with PPN Parameters
Starting from the global parametrized post-Newtonian (PPN) reference system
with two PPN parameters and we consider a space-bounded
subsystem of matter and construct a local reference system for that subsystem
in which the influence of external masses reduces to tidal effects. Both the
metric tensor of the local PPN reference system in the first post-Newtonian
approximation as well as the coordinate transformations between the global PPN
reference system and the local one are constructed in explicit form. The terms
proportional to reflecting a violation of the
equivalence principle are discussed in detail. We suggest an empirical
definition of multipole moments which are intended to play the same role in PPN
celestial mechanics as the Blanchet-Damour moments in General Relativity.
Starting with the metric tensor in the local PPN reference system we derive
translational equations of motion of a test particle in that system. The
translational and rotational equations of motion for center of mass and spin of
each of extended massive bodies possessing arbitrary multipole structure
are derived. As an application of the general equations of motion a
monopole-spin dipole model is considered and the known PPN equations of motion
of mass monopoles with spins are rederived.Comment: 71 page
Kolmogorov entropy of a dynamical system with an increasing number of degrees of freedom
none3Lyapunov characteristic numbers are used to estimate numerically the Kolmogorov entropy of an isolated one-dimensional self-gravitating system consisting of N plane parallel sheets with uniform density. It appears that the Kolmogorov entropy increases linearly when the number of degrees of freedom is greater than or equal to 2.noneG. Benettin;C. Froeschle;J. ScheideckerBenettin, Giancarlo; C., Froeschle; J., Scheidecke
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