8,540 research outputs found
On the stability of circular orbits in galactic dynamics: Newtonian thin disks
The study of off-equatorial orbits in razor-thin disks is still in its
beginnings. Contrary to what was presented in the literature in recent
publications, the vertical stability criterion for equatorial circular orbits
cannot be based on the vertical epicyclic frequency, because of the
discontinuity in the gravitational field on the equatorial plane. We present a
rigorous criterion for the vertical stability of circular orbits in systems
composed by a razor-thin disk surrounded by a smooth axially symmetric
distribution of matter, the latter representing additional structures such as
thick disk, bulge and (dark matter) halo. This criterion is satisfied once the
mass surface density of the thin disk is positive. Qualitative and quantitative
analyses of nearly equatorial orbits are presented. In particular, the analysis
of nearly equatorial orbits allows us to construct an approximate analytical
third integral of motion in this region of phase-space, which describes the
shape of these orbits in the meridional plane.Comment: 3 pages, 1 figure. In Proceedings of the MG13 Meeting on General
Relativity, Stockholm University, Sweden, 1-7 July 2012. World Scientific,
Singapore. Based on arXiv:1206.6501. in The Thirteenth Marcel Grossmann
Meeting: On Recent Developments in Theoretical and Experimental General
Relativity, Astrophysics, and Relativistic Field Theories (In 3 Volumes),
chap. 438, pages 2346-2348 (2015
Vertical stability of circular orbits in relativistic razor-thin disks
During the last few decades, there has been a growing interest in exact
solutions of Einstein equations describing razor-thin disks. Despite the
progress in the area, the analytical study of geodesic motion crossing the disk
plane in these systems is not yet so developed. In the present work, we propose
a definite vertical stability criterion for circular equatorial timelike
geodesics in static, axially symmetric thin disks, possibly surrounded by other
structures preserving axial symmetry. It turns out that the strong energy
condition for the disk stress-energy content is sufficient for vertical
stability of these orbits. Moreover, adiabatic invariance of the vertical
action variable gives us an approximate third integral of motion for oblique
orbits which deviate slightly from the equatorial plane. Such new approximate
third integral certainly points to a better understanding of the analytical
properties of these orbits. The results presented here, derived for static
spacetimes, may be a starting point to study the motion around rotating,
stationary razor-thin disks. Our results also allow us to conjecture that the
strong energy condition should be sufficient to assure transversal stability of
periodic orbits for any singular timelike hypersurface, provided it is
invariant under the geodesic flow.Comment: 13 pages, 4 figures; Accepted for publication in Physical Review
Kinematic Analysis and Trajectory Planning of the Orthoglide 5-axis
The subject of this paper is about the kinematic analysis and the trajectory
planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of
freedom parallel kinematic machine developed at IRCCyN and is made up of a
hybrid architecture, namely, a three degrees of freedom translational parallel
manip-ulator mounted in series with a two degrees of freedom parallel spherical
wrist. The simpler the kinematic modeling of the Or-thoglide 5-axis, the higher
the maximum frequency of its control loop. Indeed, the control loop of a
parallel kinematic machine should be computed with a high frequency, i.e.,
higher than 1.5 MHz, in order the manipulator to be able to reach high speed
motions with a good accuracy. Accordingly, the direct and inverse kinematic
models of the Orthoglide 5-axis, its inverse kine-matic Jacobian matrix and the
first derivative of the latter with respect to time are expressed in this
paper. It appears that the kinematic model of the manipulator under study can
be written in a quadratic form due to the hybrid architecture of the Orthoglide
5-axis. As illustrative examples, the profiles of the actuated joint angles
(lengths), velocities and accelerations that are used in the control loop of
the robot are traced for two test trajectories.Comment: Appears in International Design Engineering Technical Conferences \&
Computers and Information in Engineering Conference, Aug 2015, Boston, United
States. 201
Motion around a Monopole + Ring system: I. Stability of Equatorial Circular Orbits vs Regularity of Three-dimensional Motion
We study the motion of test particles around a center of attraction
represented by a monopole (with and without spheroidal deformation) surrounded
by a ring, given as a superposition of Morgan & Morgan discs. We deal with two
kinds of bounded orbits: (i) Equatorial circular orbits and (ii) general
three-dimensional orbits. The first case provides a method to perform a linear
stability analysis of these structures by studying the behavior of vertical and
epicyclic frequencies as functions of the mass ratio, the size of the ring
and/or the quadrupolar deformation. In the second case, we study the influence
of these parameters in the regularity or chaoticity of motion. We find that
there is a close connection between linear stability (or unstability) of
equatorial circular orbits and regularity (or chaoticity) of the
three-dimensional motion.Comment: 13 pages, 17 figures, to appear in MNRA
Typing Quantum Superpositions and Measurement
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.Fil: DĂaz Caro, Alejandro. Universidad Nacional de Quilmes. Departamento de Ciencia y TecnologĂa; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Dowek, Gilles. Institut National de Recherche en Informatique et en Automatique; Franci
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