549 research outputs found
Computer program offers new method for constructing periodic orbits in nonlinear dynamical systems
Computer program uses an iterative method to construct precisely periodic orbits which dynamically approximate solutions that converge to precise dynamical solutions in the limit of the sequence. The method used is a modification of the generalized Newton-Raphson algorithm used in analyzing two point boundary problems
Method for constructing periodic orbits in nonlinear dynamic systems
Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems
Classifying relative equilibria. III
We announce several theorems on the evolution of relative equilibria classes in the planar n-body problem. In an earlier paper [1] we announced a partial classification of relative equilibria of four equal masses. In [2] we described these new relative equilibria classes and showed the way in which a degeneracy arose in the four body problem. These results point the way toward classifying relative equilibria for any n > 4.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43204/1/11005_2004_Article_BF00405589.pd
Rosette Central Configurations, Degenerate central configurations and bifurcations
In this paper we find a class of new degenerate central configurations and
bifurcations in the Newtonian -body problem. In particular we analyze the
Rosette central configurations, namely a coplanar configuration where
particles of mass lie at the vertices of a regular -gon, particles
of mass lie at the vertices of another -gon concentric with the first,
but rotated of an angle , and an additional particle of mass lies
at the center of mass of the system. This system admits two mass parameters
and \ep=m_2/m_1. We show that, as varies, if ,
there is a degenerate central configuration and a bifurcation for every
\ep>0, while if there is a bifurcations only for some values of
.Comment: 16 pages, 6 figure
Health Information Needs of the Pregnant Adolescent
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73151/1/j.1745-7599.1994.tb00906.x.pd
Action minimizing orbits in the n-body problem with simple choreography constraint
In 1999 Chenciner and Montgomery found a remarkably simple choreographic
motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal
masses travel on a eight shaped planar curve; this orbit is obtained minimizing
the action integral on the set of simple planar choreographies with some
special symmetry constraints. In this work our aim is to study the problem of
masses moving in \RR^d under an attractive force generated by a potential
of the kind , , with the only constraint to be a simple
choreography: if are the orbits then we impose the
existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau),
i=1,...,n, t \in \RR, where . In this setting, we first
prove that for every d,n \in \NN and , the lagrangian action
attains its absolute minimum on the planar circle. Next we deal with the
problem in a rotating frame and we show a reacher phenomenology: indeed while
for some values of the angular velocity minimizers are still circles, for
others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit
Nurses Attitudes Towards the Use of Restraints in the Critical Care Setting
The use of restraints is especially prevalent in critical care units in order to decrease patients’ interference with their medical care. Although there are quality improvement studies to reduce the frequency of restraints, nurses are reluctant to implement this into their practice when considering restrint safety. Our research question states, in critical care patients, how does the nurse’s attitude and experience affect the use of restraints? There is limited education provided to nurses regarding the determinants of restraints in the acute care setting. We conducted a systematic review of literature to investigate how the attitudes of nurses affect patient outcomes in relation to restraints. We developed a practice protocol to explore the differences in the mindset of nurses and how these attitudes affected the decisions of nurses within a critical care unit
Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
We examine in detail the relative equilibria in the four-vortex problem where
two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and
\Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is
that for m > 0, the convex configurations all contain a line of symmetry,
forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for
all m but the isosceles trapezoid case exists only when m is positive. In fact,
there exist asymmetric convex configurations when m < 0. In contrast to the
Newtonian four-body problem with two equal pairs of masses, where the symmetry
of all convex central configurations is unproven, the equations in the vortex
case are easier to handle, allowing for a complete classification of all
solutions. Precise counts on the number and type of solutions (equivalence
classes) for different values of m, as well as a description of some of the
bifurcations that occur, are provided. Our techniques involve a combination of
analysis and modern and computational algebraic geometry
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