1,452 research outputs found
Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere and the hyperbolic plane
The Kepler problem is a dynamical system that is well defined not only on the
Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the
theory of central potentials on spaces of constant curvature is studied. All
the mathematical expressions are presented using the curvature \k as a
parameter, in such a way that they reduce to the appropriate property for the
system on the sphere , or on the hyperbolic plane , when
particularized for \k>0, or \k<0, respectively; in addition, the Euclidean
case arises as the particular case \k=0. In the second part we study the main
properties of the Kepler problem on spaces with curvature, we solve the
equations and we obtain the explicit expressions of the orbits by using two
different methods: first by direct integration and second by obtaining the
\k-dependent version of the Binet's equation. The final part of the article,
that has a more geometric character, is devoted to the study of the theory of
conics on spaces of constant curvature.Comment: 37 pages, 7 figure
Gipsy 3D: Analysis, Visualization and Vo-Tools
The scientific goals of the AMIGA project are based on the analysis of a
significant amount of spectroscopic 3D data. In order to perform this work we
present an initiative to develop a new VO compliant package, including present
core applications and tasks offered by the Groningen Image Processing System
(GIPSY), and new ones based on use cases elaborated in collaboration with ad-
vanced users. One of the main goals is to provide local interoperability
between GIPSY (visualization and data analysis) and other VO software. The
connectivity with the Virtual Observatory environment will provide general
access to 3D data VO archives and services, maximizing the potential for
scientific discovery.Comment: 2 pages, 1 figure, to appear in the proceedings of the
"Multi-wavelength Astronomy and Virtual Observatory" Workshop held at ESAC
1-3 Dec 200
Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces
This paper contains a thorough study of the trigonometry of the homogeneous
symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex
Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and
hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and
some non-compact symmetric spaces associated to SL(N+1,R) are the generic
members in this family. The method encapsulates trigonometry for this whole
family of spaces into a single "basic trigonometric group equation", and has
'universality' and '(self)-duality' as its distinctive traits. All previously
known results on the trigonometry of CP^N and CH^N follow as particular cases
of our general equations. The physical Quantum Space of States of any quantum
system belongs, as the complex Hermitian space member, to this parametrised
family; hence its trigonometry appears as a rather particular case of the
equations we obtain.Comment: 46 pages, LaTe
A three-dimensional view of the remnant of Nova Persei 1901 (GK Per)
We present a kinematical study of the optical ejecta of GK Per. It is based
on proper motions measurements of 282 knots from ~20 images spanning 25 years.
Doppler-shifts are also computed for 217 knots. The combination of proper
motions and radial velocities allows a unique 3-D view of the ejecta to be
obtained. The main results are: (1) the outflow is a thick shell in which knots
expand with a significant range of velocities, mostly between 600 and 1000
km/s; (2) kinematical ages indicate that knots have suffered only a modest
deceleration since their ejection a century ago; (3) no evidence for anisotropy
in the expansion rate is found; (4) velocity vectors are generally aligned
along the radial direction but a symmetric pattern of non-radial velocities is
also observed at specific directions; (5) the total Halpha+[NII] flux has been
linearly decreasing at a rate of 2.6 % per year in the last decade. The Eastern
nebular side is fading at a slower rate than the Western one. Some of the knots
displayed a rapid change of brightness during the 2004-2011 period. Over a
longer timescale, a progressive circularization and homogenization of the
nebula is taking place; (6) a kinematic distance of 400+-30 pc is determined.
These results raise some problems to the previous interpretations of the
evolution of GK Per. In particular, the idea of a strong interaction of the
outflow with the surrounding medium in the Southwest quadrant is not supported
by our data.Comment: Accepted for publication in The Astrophysical Journal (19 pages, 17
figures). Higher resolution version of this article (2.5 MB) is available at
http://www.aai.ee/~sinope/ApJ89291_liimets.pd
Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability
The existence of a Lagrangian description for the second-order Riccati
equation is analyzed and the results are applied to the study of two different
nonlinear systems both related with the generalized Riccati equation. The
Lagrangians are nonnatural and the forces are not derivable from a potential.
The constant value of a preserved energy function can be used as an
appropriate parameter for characterizing the behaviour of the solutions of
these two systems. In the second part the existence of two--dimensional
versions endowed with superintegrability is proved. The explicit expressions of
the additional integrals are obtained in both cases. Finally it is proved that
the orbits of the second system, that represents a nonlinear oscillator, can be
considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure
Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the
Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is
considered from the perspective of the radial Schr\"odinger equations on 3D
spaces of any (either positive, zero or negative) constant curvature. Further
to Stevenson, we show in detail how to get the hypergeometric wavefunction for
the hydrogen atom case. Finally, we make a comparison between the ``space
curvature" effects and minimal length effects for the hydrogen spectrumComment: 6 pages, v
Morpho-kinematical modelling in the molecular zoo beyond CO: the case of M 1-92
Ongoing improvements of sub-mm- and mm-range interferometers and single-dish
radiotelescopes are progressively allowing the detailed study of planetary
nebulae (PNe) in molecular species other than 12CO and 13CO. We are
implementing a new set of tables for extending the capabilities of the
morpho-kinematical modelling tool SHAPE+shapemol, so radiative transfer in
molecular species beyond 12CO and 13CO, namely C17O, C18O, HCN, HNC, CS, SiO,
HCO+, and N2H+, are enabled under the Large Velocity Gradient approximation
with the ease of use of SHAPE. We present preliminary results on the
simultaneous analysis of a plethora of IRAM-30m and HERSCHEL/HIFI spectra, and
NOEMA maps of different species in the pre-PN nebula M~1-92, which show
interesting features such as a previously undetected pair of polar, turbulent,
high-temperature blobs, or a 17O/18O isotopic ratio of 1.7, which indicates the
AGB should have turned C-rich, as opposed to the apparent nature of its O-rich
nebula.Comment: To be published in the Proceedings of the IAU Symposium 384; 6 pages,
5 figures, 1 tabl
Informe acerca del museo nacional
Informe dirigido al rector de la Universidad Nacional, quien comisiona a Rafael Santander, para realizar una visita de inspección al Museo Nacional. Bogotá, octubre de 1868
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