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991.
992.
B. Barbanis 《Celestial Mechanics and Dynamical Astronomy》1993,55(1):87-98
Various sets of periodic solutions of a 3-D Hamiltonian system crossing perpendicularly thez=0 plane are presented. These sets form a main multi-spiral pattern and two secondary ones which have three focal points. The main pattern is inside a stochastic region that surrounds a simple complex unstable periodic orbit, while the two secondary patterns are parts of a stochastic sea. Through these regions the stochastic region communicates with the stochastic sea. 相似文献
993.
Vadim A. Antonov Faziliddin T. Shamshiev 《Celestial Mechanics and Dynamical Astronomy》1993,56(3):451-469
This paper deals with the plane motion of a star in the gravitational field of a system which is in a steady state and rotates with a constant angular velocity. For these systems a class of potentials permitting a local integral, linear with respect to the velocity components, has been found. The concept of the local integral itself was introduced by one of the authors of the present paper (Antonov, 1981). A detailed model has been constructed. The corresponding domain of the particle motion and the form of the trajectory coils have been determined. The result is compared with the motion in a more realistic potential. 相似文献
994.
N. D. Caranicolas 《Celestial Mechanics and Dynamical Astronomy》1989,47(1):87-96
We derive an algebraic mapping for an autonomous, two-dimensional galactic type Hamiltonian in the 1/1 resonance case. We use the mapping to study the stability of the periodic orbits. Using the x — p
x
Poincaré surface section, we compare the results of the mapping with those found by the numerical integration of the full equations of motion. For small values of the perturbation the results of the two methods are in very good agreement while satisfactory agreement is obtained for larger perturbations. 相似文献
995.
996.
Roberto O. Aquilano Juan C. Muzzio Hugo D. Navone Alejandra F. Zorzi 《Celestial Mechanics and Dynamical Astronomy》2007,99(4):307-324
We used a multipolar code to create, through the dissipationless collapses of systems of 1,000,000 particles, three self-consistent
triaxial stellar systems with axial ratios corresponding to those of E4, E5 and E6 galaxies. The E5 and E6 models have small,
but significant, rotational velocities although their total angular momenta are zero, that is, they exhibit figure rotation;
the rotational velocity decreases with decreasing flattening of the models and for the E4 model it is essentially zero. Except
for minor changes, probably caused by unavoidable relaxation effects, the systems are highly stable. The potential of each
system was subsequently approximated with interpolating formulae yielding smooth potentials, stationary for the non-rotating
model and stationary in the rotating frame for the rotating ones. The Lyapunov exponents could then be computed for randomly
selected samples of the bodies that make up the different systems, allowing the recognition of regular and partially and fully
chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using their locations on the frequency map.
As it could be expected, the percentages of chaotic orbits increase with the flattening of the system. As one goes from E6
through E4, the fraction of partially chaotic orbits relative to that of fully chaotic ones increases, with the former surpassing
the latter in model E4; the likely cause of this behavior is that triaxiality diminishes from E6 through E4, the latter system
being almost axially symmetric. We especulate that some of the partially chaotic orbits may obey a global integral akin to
the long axis component of angular momentum. Our results show that is perfectly possible to have highly stable triaxial models
with large fractions of chaotic orbits, but such systems cannot have constant axial ratios from center to border: a slightly
flattened reservoir of highly chaotic orbits seems to be mandatory for those systems. 相似文献
997.
In this paper, an arbitrary Lagrangian–Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore‐water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated‐Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
998.
Prasenjit Sengupta Srinivas R. Vadali Kyle T. Alfriend 《Celestial Mechanics and Dynamical Astronomy》2007,97(2):101-129
This paper develops a tensor and its inverse, for the analytical propagation of the position and velocity of a satellite,
with respect to another, in an eccentric orbit. The tensor is useful for relative motion analysis where the separation distance
between the two satellites is large. The use of nonsingular elements in the formulation ensures uniform validity even when
the reference orbit is circular. Furthermore, when coupled with state transition matrices from existing works that account
for perturbations due to Earth oblateness effects, its use can very accurately propagate relative states when oblateness effects
and second-order nonlinearities from the differential gravitational field are of the same order of magnitude. The effectiveness
of the tensor is illustrated with various examples. 相似文献
999.
A simple approximate model of the asteroid dynamics near the 3:1 mean–motion resonance with Jupiter can be described by a
Hamiltonian system with two degrees of freedom. The phase variables of this system evolve at different rates and can be subdivided
into the ‘fast’ and ‘slow’ ones. Using the averaging technique, wisdom obtained the evolutionary equations which allow to
study the long-term behavior of the slow variables. The dynamic system described by the averaged equations will be called
the ‘Wisdom system’ below. The investigation of the, wisdom system properties allows us to present detailed classification
of the slow variables’ evolution paths. The validity of the averaged equations is closely connected with the conservation
of the approximate integral (adiabatic invariant) possessed by the original system. Qualitative changes in the behavior of
the fast variables cause the violations of the adiabatic invariance. As a result the adiabatic chaos phenomenon takes place.
Our analysis reveals numerous stable periodic trajectories in the region of the adiabatic chaos. 相似文献
1000.