211 research outputs found
Methods of regularization for computing orbits in celestial mechanics
Numerical and analytical methods for orbit computation in celestial mechanics during and beyond collision by introduction of regularized coordinate
Human Like Adaptation of Force and Impedance in Stable and Unstable Tasks
Abstract—This paper presents a novel human-like learning con-troller to interact with unknown environments. Strictly derived from the minimization of instability, motion error, and effort, the controller compensates for the disturbance in the environment in interaction tasks by adapting feedforward force and impedance. In contrast with conventional learning controllers, the new controller can deal with unstable situations that are typical of tool use and gradually acquire a desired stability margin. Simulations show that this controller is a good model of human motor adaptation. Robotic implementations further demonstrate its capabilities to optimally adapt interaction with dynamic environments and humans in joint torque controlled robots and variable impedance actuators, with-out requiring interaction force sensing. Index Terms—Feedforward force, human motor control, impedance, robotic control. I
Intrinsic Geometry of a Null Hypersurface
We apply Cartan's method of equivalence to construct invariants of a given
null hypersurface in a Lorentzian space-time. This enables us to fully classify
the internal geometry of such surfaces and hence solve the local equivalence
problem for null hypersurface structures in 4-dimensional Lorentzian
space-times
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
The interaction of a spin 1/2 particle (described by the non-relativistic
"Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied.
It is shown, that similarly to the four dimensional spinor models, there is a
consistent possibility of coupling them also by axial or chiral type currents.
Static self dual vortex solutions together with a vortex-lattice are found with
the new couplings.Comment: Plain TEX, 10 page
A Simple fMRI Compatible Robotic Stimulator to Study the Neural Mechanisms of Touch and Pain.
This paper presents a simple device for the investigation of the human somatosensory system with functional magnetic imaging (fMRI). PC-controlled pneumatic actuation is employed to produce innocuous or noxious mechanical stimulation of the skin. Stimulation patterns are synchronized with fMRI and other relevant physiological measurements like electroencephalographic activity and vital physiological parameters. The system allows adjustable regulation of stimulation parameters and provides consistent patterns of stimulation. A validation experiment demonstrates that the system safely and reliably identifies clusters of functional activity in brain regions involved in the processing of pain. This new device is inexpensive, portable, easy-to-assemble and customizable to suit different experimental requirements. It provides robust and consistent somatosensory stimulation, which is of crucial importance to investigating the mechanisms of pain and its strong connection with the sense of touch
Conformal Properties of Chern-Simons Vortices in External Fields
The construction and the symmetries of Chern-Simons vortices in harmonic and
uniform magnetic force backgrounds found by Ezawa, Hotta and Iwazaki, and by
Jackiw and Pi are generalized using the non-relativistic Kaluza-Klein-type
framework presented in our previous paper. All Schrodinger-symmetric
backgrounds are determined.Comment: 10 pages,CPT-94/p.3028, te
Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-time
A classification of all possible realizations of the Galilei,
Galilei-similitude and Schroedinger Lie algebras in three-dimensional
space-time in terms of vector fields under the action of the group of local
diffeomorphisms of the space \R^3\times\C is presented. Using this result a
variety of general second order evolution equations invariant under the
corresponding groups are constructed and their physical significance are
discussed
Celestial Mechanics, Conformal Structures, and Gravitational Waves
The equations of motion for non-relativistic particles attracting
according to Newton's law are shown to correspond to the equations for null
geodesics in a -dimensional Lorentzian, Ricci-flat, spacetime with a
covariantly constant null vector. Such a spacetime admits a Bargmann structure
and corresponds physically to a generalized pp-wave. Bargmann electromagnetism
in five dimensions comprises the two Galilean electro-magnetic theories (Le
Bellac and L\'evy-Leblond). At the quantum level, the -body Schr\"odinger
equation retains the form of a massless wave equation. We exploit the conformal
symmetries of such spacetimes to discuss some properties of the Newtonian
-body problem: homographic solutions, the virial theorem, Kepler's third
law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal
Killing 2-tensors, and motions under inverse square law forces with a
gravitational constant varying inversely as time (Dirac). The latter
problem is reduced to one with time independent forces for a rescaled position
vector and a new time variable; this transformation (Vinti and Lynden-Bell)
arises from a conformal transformation preserving the Ricci-flatness
(Brinkmann). A Ricci-flat metric representing non-relativistic
gravitational dyons is also pointed out. Our results for general time-dependent
are applicable to the motion of point particles in an expanding
universe. Finally we extend these results to the quantum regime.Comment: 26 pages, LaTe
Newton-Hooke spacetimes, Hpp-waves and the cosmological constant
We show explicitly how the Newton-Hooke groups act as symmetries of the
equations of motion of non-relativistic cosmological models with a cosmological
constant. We give the action on the associated non-relativistic spacetimes and
show how these may be obtained from a null reduction of 5-dimensional
homogeneous pp-wave Lorentzian spacetimes. This allows us to realize the
Newton-Hooke groups and their Bargmann type central extensions as subgroups of
the isometry groups of the pp-wave spacetimes. The extended Schrodinger type
conformal group is identified and its action on the equations of motion given.
The non-relativistic conformal symmetries also have applications to
time-dependent harmonic oscillators. Finally we comment on a possible
application to Gao's generalization of the matrix model.Comment: 21 page
(1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups
All Lie bialgebra structures for the (1+1)-dimensional centrally extended
Schrodinger algebra are explicitly derived and proved to be of the coboundary
type. Therefore, since all of them come from a classical r-matrix, the complete
family of Schrodinger Poisson-Lie groups can be deduced by means of the
Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended
Galilei and gl(2) Lie bialgebras within the Schrodinger classification are
studied. As an application, new quantum (Hopf algebra) deformations of the
Schrodinger algebra, including their corresponding quantum universal
R-matrices, are constructed.Comment: 25 pages, LaTeX. Possible applications in relation with integrable
systems are pointed; new references adde
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