494 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
A note on independent variables for restricted three-body problems
In studies of the elliptic restricted three-body problem, the true anomaly of the motion of the primaries is often used as the independent variable. The equations of motion then show invariancy in form from the circular case. It is of interest whether other independent variables exist, such that the invariant form of the equations is maintained. It is found that true anomaly is the only such variable.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42558/1/10569_2005_Article_BF01231394.pd
Capture of dark matter by the Solar System. Simple estimates
We consider the capture of galactic dark matter by the Solar System, due to
the gravitational three-body interaction of the Sun, a planet, and a dark
matter particle. Simple estimates are presented for the capture cross-section,
as well as for density and velocity distribution of captured dark matter
particles close to the Earth.Comment: 5 page
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
A possible third component in the L dwarf binary system DENIS-P J020529.0-115925 discovered with the Hubble Space Telescope
We present results showing that the multiple system DENIS-P J020529.0-115925
is likely to be a triple system of brown dwarfs. The secondary of this
previously known binary system shows a clear elongation on six images obtained
at six different epochs. Significant residuals remain after PSF subtraction on
these images, characteristic of multiplicity, and indicating that the secondary
is probably a double itself. Dual-PSF fitting shows that the shape of the
secondary is consistent with that of a binary system. These measurements show
that the probability that DENIS-P J020529.0-115925 is a triple system is very
high. The photometric and spectroscopic properties of the system are consistent
with the presence of three components with spectral types L5, L8 and T0.Comment: 15 pages, 3 tables, 6 figures, accepted for publication in AJ. High
resolution version available at
ftp://ftp.mpe.mpg.de/people/hbouy/publications/denis0205.ps.g
New periodic orbits in the solar sail three-body problem
We identify displaced periodic orbits in the circular restricted three-body problem, wher the third (small) body is a solar sail. In particular, we consider solar sail orbits in the earth-sun system which are high above the exliptic plane. It is shown that periodic orbits about surfaces of artificial equilibria are naturally present at linear order. Using the method of Lindstedt-Poincare, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the solar sail elliptical restricted three-body problem. A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e=0 and continuing to the requied eccentricity of e=0.0167. The stability of these periodic orbits is investigated
Phase space structures and ionization dynamics of hydrogen atom in elliptically polarized microwaves
The multiphoton ionization of hydrogen atoms in a strong elliptically
polarized microwave field exhibits complex features that are not observed for
ionization in circular and linear polarized fields. Experimental data reveal
high sensitivity of ionization dynamics to the small changes of the field
polarization. The multidimensional nature of the problem makes widely used
diagnostics of dynamics, such as Poincar\'{e} surfaces of section, impractical.
We analyze the phase space dynamics using finite time stability analysis
rendered by the fast Lyapunov Indicators technique. The concept of
zero--velocity surface is used to initialize the calculations and visualize the
dynamics. Our analysis provides stability maps calculated for the initial
energy at the maximum and below the saddle of the zero-velocity surface. We
estimate qualitatively the dependence of ionization thresholds on the
parameters of the applied field, such as polarization and scaled amplitude
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
`Similar' coordinate systems and the Roche geometry. Application
A new equivalence relation, named relation of 'similarity' is defined and
applied in the restricted three-body problem. Using this relation, a new class
of trajectories (named 'similar' trajectories) are obtained; they have the
theoretical role to give us new details in the restricted three-body problem.
The 'similar' coordinate systems allow us in addition to obtain a unitary and
an elegant demonstration of some analytical relations in the Roche geometry. As
an example, some analytical relations published in Astrophysical Journal by
Seidov in 2004 are demonstrated.Comment: 9 pages (preprint format), 9 figures, published in Astrophysics and
Space Scienc
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