6,587 research outputs found
Relative equilibria for the generalized rigid body
This paper gives necessary and sufficient conditions for the (n-dimensional)
generalized free rigid body to be in a state of relative equilibrium. The
conditions generalize those for the case of the three-dimensional free rigid body,
namely that the body is in relative equilibrium if and only if its angular velocity
and angular momentum align, that is, if the body rotates about one of its
principal axes. For the n-dimensional rigid body in the Manakov formulation,
these conditions have a similar interpretation. We use this result to state and
prove a generalized Saari’s Conjecture (usually stated for the N-body problem)
for the special case of the generalized rigid body
Discrete Routh Reduction
This paper develops the theory of abelian Routh reduction for discrete
mechanical systems and applies it to the variational integration of mechanical
systems with abelian symmetry. The reduction of variational Runge-Kutta
discretizations is considered, as well as the extent to which symmetry
reduction and discretization commute. These reduced methods allow the direct
simulation of dynamical features such as relative equilibria and relative
periodic orbits that can be obscured or difficult to identify in the unreduced
dynamics. The methods are demonstrated for the dynamics of an Earth orbiting
satellite with a non-spherical correction, as well as the double
spherical pendulum. The problem is interesting because in the unreduced
picture, geometric phases inherent in the model and those due to numerical
discretization can be hard to distinguish, but this issue does not appear in
the reduced algorithm, where one can directly observe interesting dynamical
structures in the reduced phase space (the cotangent bundle of shape space), in
which the geometric phases have been removed. The main feature of the double
spherical pendulum example is that it has a nontrivial magnetic term in its
reduced symplectic form. Our method is still efficient as it can directly
handle the essential non-canonical nature of the symplectic structure. In
contrast, a traditional symplectic method for canonical systems could require
repeated coordinate changes if one is evoking Darboux' theorem to transform the
symplectic structure into canonical form, thereby incurring additional
computational cost. Our method allows one to design reduced symplectic
integrators in a natural way, despite the noncanonical nature of the symplectic
structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added,
fixed typo
Kinetic energy functional for Fermi vapors in spherical harmonic confinement
Two equations are constructed which reflect, for fermions moving
independently in a spherical harmonic potential, a differential virial theorem
and a relation between the turning points of kinetic energy and particle
densities. These equations are used to derive a differential equation for the
particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure
Transport and stirring induced by vortex formation
The purpose of this study is to analyse the transport and stirring of fluid that occurs owing to the formation and growth of a laminar vortex ring. Experimental data was collected upstream and downstream of the exit plane of a piston-cylinder apparatus by particle-image velocimetry. This data was used to compute Lagrangian coherent structures to demonstrate how fluid is advected during the transient process of vortex ring formation. Similar computations were performed from computational fluid dynamics (CFD) data, which showed qualitative agreement with the experimental results, although the CFD data provides better resolution in the boundary layer of the cylinder. A parametric study is performed to demonstrate how varying the piston-stroke length-to-diameter ratio affects fluid entrainment during formation. Additionally, we study how regions of fluid are stirred together during vortex formation to help establish a quantitative understanding of the role of vortical flows in mixing. We show that identification of the flow geometry during vortex formation can aid in the determination of efficient stirring. We compare this framework with a traditional stirring metric and show that the framework presented in this paper is better suited for understanding stirring/mixing in transient flow problems. A movie is available with the online version of the paper
Low energy proton bidirectional anisotropies and their relation to transient interplanetary magnetic structures: ISEE-3 observations
It is known that the interplanetary medium in the period approaching solar maximum is characterized by an enhancement in the occurrence of transient solar wind streams and shocks and that such systems are often associated with looplike magnetic structures or clouds. There is observational evidence that bidirectional, field aligned flows of low energy particles could be a signature of such looplike structures, although detailed models for the magnetic field configuration and injection mechanisms do not exist at the current time. Preliminary results of a survey of low energy proton bidirectional anisotropies measured on ISEE-3 in the interplanetary medium between August 1978 and May 1982, together with magnetic field data from the same spacecraft are presented
Variational Principles for Lagrangian Averaged Fluid Dynamics
The Lagrangian average (LA) of the ideal fluid equations preserves their
transport structure. This transport structure is responsible for the Kelvin
circulation theorem of the LA flow and, hence, for its convection of potential
vorticity and its conservation of helicity.
Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational
framework that implies the LA fluid equations. This is expressed in the
Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated
for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure
Cometary Astrometry
Modern techniques for making cometary astrometric observations, reducing these observations, using accurate reference star catalogs, and computing precise orbits and ephemerides are discussed in detail and recommendations and suggestions are given in each area
An update on informed consent and the effect on the clinical practice of those working with people with a learning disability
In people with learning disability who have capacity under the Mental Capacity Act 2005 health professionals need to ensure that, when they are giving consent to treatment with medication, the consent is truly ‘informed’. The judgment of Montgomery v Lanarkshire Health Board [2015] and the Accessible Information Standard (NHS England 2016) seek to clarify this position which affects learning disability nurses as well as other healthcare professionals. This article examines how the law affects the way information is provided to service users. For people without capacity ‘Best Interests’ will continue to be applied
Modelling Basal Area of Perennial Grasses in Australian Semi-Arid Wooded Grasslands
In many semi-arid pastoral systems, landscape processes easily become dysfunctional. Shifts to less functional states may be irreversible, and have long-term consequences for pastoral profitability and social viability of rural communities. Typically, shifts to lower functional states involve a decline in perennial grasses (Hodgkinson, 1994). Here we develop a conceptual basis for modelling the basal area of perennial grasses in a semi-arid grassland and validate the model using data from a 10-year grazing study
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