365 research outputs found
Trajectory optimization using regularized variables
Regularized equations for a particular optimal trajectory are compared with unregularized equations with respect to computational characteristics, using perturbation type numerical optimization. In the case of the three dimensional, low thrust, Earth-Jupiter rendezvous, the regularized equations yield a significant reduction in computer time
Foundations of multiple black hole evolutions
We present techniques for long-term, stable, and accurate evolutions of
multiple-black-hole spacetimes using the `moving puncture' approach with
fourth- and eighth-order finite difference stencils. We use these techniques to
explore configurations of three black holes in a hierarchical system consisting
of a third black hole approaching a quasi-circular black-hole binary, and find
that, depending on the size of the binary, the resulting encounter may lead to
a prompt merger of all three black holes, production of a highly elliptical
binary (with the third black hole remaining unbound), or disruption of the
binary (leading to three free black holes). We also analyze the classical
Burrau three-body problem using full numerical evolutions. In both cases, we
find behaviors distinctly different from Newtonian predictions, which has
important implications for N-body black-hole simulations. For our simulations
we use analytic approximate data. We find that the eighth-order stencils
significantly reduce the numerical errors for our choice of grid sizes, and
that the approximate initial data produces the expected waveforms (after a
rescaling of the puncture masses) for black-hole binaries with modest initial
separations.Comment: Revtex 4, 13 pages, 15 figure
Orbital Stability of Planets in Binary Systems: A New Look at Old Results
About half of all known stellar systems with Sun-like stars consist of two or
more stars, significantly affecting the orbital stability of any planet in
these systems. This observational evidence has prompted a large array of
theoretical research, including the derivation of mathematically stringent
criteria for the orbital stability of planets in stellar binary systems, valid
for the "coplanar circular restricted three-body problem". In the following, we
use these criteria to explore the validity of results from previous theoretical
studies.Comment: 3 pages, 1 figure; submitted to: Exoplanets: Detection, Formation and
Dynamics, IAU Symposium 249, eds. Y.-S. Sun, S. Ferraz-Mello, and J.-L. Zhou
(Cambridge: Cambridge University Press
Extracting Multidimensional Phase Space Topology from Periodic Orbits
We establish a hierarchical ordering of periodic orbits in a strongly coupled
multidimensional Hamiltonian system. Phase space structures can be
reconstructed quantitatively from the knowledge of periodic orbits alone. We
illustrate our findings for the hydrogen atom in crossed electric and magnetic
fields.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let
Hydrogen atom in crossed electric and magnetic fields: Phase space topology and torus quantization via periodic orbits
A hierarchical ordering is demonstrated for the periodic orbits in a strongly
coupled multidimensional Hamiltonian system, namely the hydrogen atom in
crossed electric and magnetic fields. It mirrors the hierarchy of broken
resonant tori and thereby allows one to characterize the periodic orbits by a
set of winding numbers. With this knowledge, we construct the action variables
as functions of the frequency ratios and carry out a semiclassical torus
quantization. The semiclassical energy levels thus obtained agree well with
exact quantum calculations
Straight Line Orbits in Hamiltonian Flows
We investigate periodic straight-line orbits (SLO) in Hamiltonian force
fields using both direct and inverse methods. A general theorem is proven for
natural Hamiltonians quadratic in the momenta in arbitrary dimension and
specialized to two and three dimension. Next we specialize to homogeneous
potentials and their superpositions, including the familiar H\'enon-Heiles
problem. It is shown that SLO's can exist for arbitrary finite superpositions
of -forms. The results are applied to a family of generalized H\'enon-Heiles
potentials having discrete rotational symmetry. SLO's are also found for
superpositions of these potentials.Comment: laTeX with 6 figure
Mapping the Secular Resonance for Retrograde Irregular Satellites
Constructing dynamical maps from the filtered output of numerical
integrations, we analyze the structure of the secular resonance for
fictitious irregular satellites in retrograde orbits. This commensurability is
associated to the secular angle , where
is the longitude of pericenter of the satellite and
corresponds to the (fixed) planetocentric orbit of the Sun. Our study is
performed in the restricted three-body problem, where the satellites are
considered as massless particles around a massive planet and perturbed by the
Sun. Depending on the initial conditions, the resonance presents a diversity of
possible resonant modes, including librations of around zero (as found
for Sinope and Pasiphae) or 180 degrees, as well as asymmetric librations (e.g.
Narvi). Symmetric modes are present in all giant planets, although each regime
appears restricted to certain values of the satellite inclination. Asymmetric
solutions, on the other hand, seem absent around Neptune due to its almost
circular heliocentric orbit. Simulating the effects of a smooth orbital
migration on the satellite, we find that the resonance lock is preserved as
long as the induced change in semimajor axis is much slower compared to the
period of the resonant angle (adiabatic limit). However, the librational mode
may vary during the process, switching between symmetric and asymmetric
oscillations. Finally, we present a simple scaling transformation that allows
to estimate the resonant structure around any giant planet from the results
calculated around a single primary mass.Comment: 11 pages, 13 figure
Trajectory and stability of Lagrangian point in the Sun-Earth system
This paper describes design of the trajectory and analysis of the stability
of collinear point in the Sun-Earth system. The modified restricted three
body problem with additional gravitational potential from the belt is used as
the model for the Sun-Earth system. The effect of radiation pressure of the Sun
and oblate shape of the Earth are considered. The point is asymptotically
stable upto a specific value of time correspond to each set of values of
parameters and initial conditions. The results obtained from this study would
be applicable to locate a satellite, a telescope or a space station around the
point .Comment: Accepted for publication in Astrophysics & Space Scienc
Capture of dark matter by the Solar System
We study the capture of galactic dark matter by the Solar System. The effect
is due to the gravitational three-body interaction between the Sun, one of the
planets, and a dark matter particle. The analytical estimate for the capture
cross-section is derived and the upper and lower bounds for the total mass of
the captured dark matter particles are found. The estimates for their density
are less reliable. The most optimistic of them give an enhancement of dark
matter density by about three orders of magnitudes compared to its value in our
Galaxy. However, even this optimistic value remains below the best present
observational upper limits by about two orders of magnitude.Comment: 5 pages, 3 tables; Refs. updated and discussion extende
Linear Stability of Equilibrium Points in the Generalized Photogravitational Chermnykh's Problem
The equilibrium points and their linear stability has been discussed in the
generalized photogravitational Chermnykh's problem. The bigger primary is being
considered as a source of radiation and small primary as an oblate spheroid.
The effect of radiation pressure has been discussed numerically. The collinear
points are linearly unstable and triangular points are stable in the sense of
Lyapunov stability provided . The effect of
gravitational potential from the belt is also examined. The mathematical
properties of this system are different from the classical restricted three
body problem
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