Periodic orbit. Medical search. Frequent questions

Isaac Newton's three-body problem, which examines how three bodies affected by gravitation will orbit around each other, is well known in nonlinear dynamics and applied mathematics. (eurekalert.org)
In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. (wikipedia.org)

On the stability of the three classes of Newtonian three-body planar periodic orbits. (eurekalert.org)
Korsch & Lang, 1991] and often categorize the stability of periodic orbits. (researchgate.net)
In this paper, we provide a sufficient condition for the global stability of a periodic orbit using the contraction mapping theorem. (umn.edu)
Varigonda, S & Georgiou, TT 2000, ' Global stability of periodic orbits in relay feedback systems ', Proceedings of the IEEE Conference on Decision and Control , vol. 4, pp. 3843-3847. (umn.edu)
A conspicuous configuration is found for tethers rotating parallel to the plane of the primaries, a case in which the attitude of the tether satellite remains constant on average, and it is demonstrated that either lengthening or shortening the tether may lead to orbit stability. (uc3m.es)
Promising results are found for orbits of the vertical family, but regions of stability are also found in the case of halo orbits. (uc3m.es)
This paper considers an application of a local theory of exponentially asymptotically stability of nonsmooth periodic orbits derived from a planar dynamical system of autonomous ordinary differential equations with discontinuous right-hand side. (brighton.ac.uk)
Stiefenhofer, P & Giesl, P 2019, ' A local stability theory of nonsmooth periodic orbits: example II ', Applied Mathematical Sciences , vol. 13, no. 11. (brighton.ac.uk)
Melnikov, V. K., 1963: On the stability of the center for time periodic perturbations. (ametsoc.org)
They have identical topological properties, in particular the same number of fixed points and periodic orbits of the same stability types. (scholarpedia.org)

Most papers I have found focus mainly on Halo orbits (see example ) but I haven't found any that focus on the planar Lyapunov family. (gatewayapothecary.com)
This paper deals with the planar transfer problems (orbit raising and de-orbiting) for co-planar satellites with low-thrust propulsion, taking the self-induced collision avoidance into consideration at the mission design stage. (researchgate.net)
Bertozzi, A., 1988: Heteroclinic orbits and chaotic dynamics in planar fluid flows. (ametsoc.org)

We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. (aimsciences.org)
Science orbit design with a quasi-frozen beta angle: Effects of body obliquity on J2-perturbed dynamics. (purdue.edu)

Yet now, two researchers at Shanghai Jiao Tong University, in the eastern Chinese coastal city of Shanghai, report that at least 7 of these newly discovered families of orbits are unstable. (eurekalert.org)
In a new study published in the Beijing-based journal SCIENCE CHINA - Physics, Mechanics & Astronomy , Li Xiaoming and Liao Shijun state: "It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time, and are thus most possibly unstable at least. (eurekalert.org)
In the new study, Li and Liao used the CNS with the high-enough Taylor series method to stringently check the 13 new families of periodic orbits discovered by Milovan Šuvakov and Veljko Dmitrašinović, but found that seven of these families greatly depart from periodic orbits across a long interval of time, and are thus most possibly unstable. (eurekalert.org)
In these pieces of literatures, adjustment speed or other parameters are taken as bifurcation parameters, and complex results such as period doubling bifurcation, unstable period orbits, and chaos are found. (hindawi.com)

In general, orbits described by the three-body problem are non-periodic, i.e. chaotic, and are rather sensitive to initial conditions. (eurekalert.org)
Therefore, it is rather difficult to gain reliable convergent numerical simulations of chaotic orbits of three-body systems across a long interval of time. (eurekalert.org)
An orbit can also be chaotic. (wikipedia.org)
A resummed formula for the Wigner function, corresponding to an eigenfunction of a chaotic system, in terms of periodic orbits, is developed. (huji.ac.il)
Agam, O & Fishman, S 1993, ' Quantum eigenfunctions in terms of periodic orbits of chaotic systems ', Journal of Physics A: General Physics , vol. 26, no. 9, 010, pp. 2113-2137. (huji.ac.il)

Such orbits are not closed because they never truly repeat, but they become arbitrarily close to a repeating orbit. (wikipedia.org)
These orbits come arbitrarily close to the initial point, but fail to ever converge to a periodic orbit. (wikipedia.org)

Parameterization of invariant manifolds for periodic orbits (I): efficient numerics via the Floquet normal form. (fau.edu)

As a first step, the characterization problem is considered for all initial conditions that constitute periodic solutions of the nonlinear equations of relative motion. (elsevierpure.com)

A periodic behavior is a well observed phenomena in biological and economical systems. (aimsciences.org)
We also examine a periodic behavior of evolutionary games on graphs with the underlying graph being an acyclic (tree) graph. (aimsciences.org)
Astonishingly, even this acyclic structure allows for arbitrary long periodic behavior. (aimsciences.org)
We investigate the periodic behavior of the verticals of an orbit of the cellular automaton and establish that there exists, depending on the characteristic of the field, a universal behavior for the evolution of periodic verticals. (episciences.org)

Stars that host orbiting planets may display periodic dips of light each time a planet crosses, or transits, the star. (sciencedaily.com)

An orbit can be hyperbolic if nearby points approach or diverge from the orbit exponentially fast. (wikipedia.org)
We present an efficient numerical method for computing Fourier-Taylor expansions of (un)stable manifolds associated with hyperbolic periodic orbits. (fau.edu)

The known periodic solutions that are modified in the case of tether satellites are discussed with a focus on the Hill problem. (uc3m.es)
On any clear evening within a couple of hours of local sunset and with no optical aid, you can usually spot several Earth-orbiting satellites creeping across the sky like moving stars. (space.com)
Even without human threats to SATCOM, periodic geomagnetic storms can damage satellites in orbit. (ausa.org)

How can you construct the periodic orbits around libration points L1 and L2 in the circular restricted three-body problem and prove their existence? (gatewayapothecary.com)
This result excludes the existence of periodic orbits for some models that describe intraspecific and / or interspecific competition, relationships of competition, predation and capture of individuals of any of the species. (scielo.sa.cr)
We establish the existence of periodic orbits of seasonal SIQRS disease, by using Leray-Schauder degree theory. (txstate.edu)

In 2013, physicists Milovan Šuvakov and Veljko Dmitrašinović at the Institute of Physics in Belgrade reported: "We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. (eurekalert.org)
The group, led by physics professor emeritus Saul Rappaport, determined that in order for the planet to maintain its extremely tight orbit around its star, it would have to be incredibly dense, made almost entirely of iron -- otherwise, the immense tidal forces from the nearby star would rip the planet to pieces. (sciencedaily.com)
To pick out those signals associated with actual planets, physics graduate student Roberto Sanchis-Ojeda searched through the set of periodic light curves, looking for frequent smaller dips in the data midway between the planetary transits. (sciencedaily.com)

As a phase space trajectory is uniquely determined for any given set of phase space coordinates, it is not possible for different orbits to intersect in phase space, therefore the set of all orbits of a dynamical system is a partition of the phase space. (wikipedia.org)
Critical orbit of discrete dynamical system based on complex quadratic polynomial. (wikipedia.org)

Using the property of null controllability with vanishing energy of the Tschauner-Hempel equations, suboptimal controllers are designed via the differential Riccati equation of the linear regulator theory of periodic systems. (elsevierpure.com)
The general theory is illustrated in the context of algebraic equations and boundary-value problems, with emphasis on periodic orbits in smooth and hybrid dynamical systems, and quasiperiodic invariant tori of flows. (illinois.edu)

We use Dulac criterion to prove the nonexistence of periodic orbits for a class of general predator-prey system with strong Allee effect in the prey population growth. (wm.edu)

Due to this, it is also difficult to find periodic orbits of three-body systems by means of numerical methods. (eurekalert.org)

A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class," the two physicists added. (eurekalert.org)
Understanding the properties of orbits by using topological methods is one of the objectives of the modern theory of dynamical systems. (wikipedia.org)

The classes are defined by the orbits geometric and algebraic symmetries. (eurekalert.org)

Analysis of Autonomous Orbit Determination in Various Near-Moon Periodic Orbits. (purdue.edu)

They exhibit sensitive dependence on initial conditions, meaning that small differences in the initial value will cause large differences in future points of the orbit. (wikipedia.org)
If the sub-circuit \(N\) consists of resistors and dependent sources, it can be replaced with the Thevenin equivalent sub-circuit and the circuit can exhibit periodic waveforms as shown in Fig. 1 (b). (scholarpedia.org)
The method essentially whittles the field to those light curves that are periodic, or that exhibit a repetitive pattern. (sciencedaily.com)

Conditions are presented which guarantee the blue sky catastrophe: the appearance of a stable periodic orbit L μ which exists for any small positive values of μ but its length and period unboundedly increase as μ → + 0. (wias-berlin.de)
We report a stable 123.4-minute periodic variation in the strength and shape of the Ca II emission line profiles originating from the debris disc around the white dwarf SDSS J122859.93+104032.9. (lu.se)

We generalize to arbitrary manifolds with elliptic periodic geodesics a quasimode construction for the nonlinear Schrödinger equation first discovered by the last author. (illinois.edu)
We also discuss computations of cycle-to-cycle connecting orbits which exploit these manifolds. (fau.edu)

at least 608 periodic orbits for sp eciﬁc parameters values. (researchgate.net)
Under the condition that the inertial orbits of the leader and a follower are coplanar, initial conditions of all periodic relative orbits are generated in terms of parameters of their orbits and their initial positions. (elsevierpure.com)

A basic classification of orbits is constant orbits or fixed points periodic orbits non-constant and non-periodic orbits An orbit can fail to be closed in two ways. (wikipedia.org)

In his book "Philosophiæ Naturalis Principia Mathematica," published more than three centuries ago, Newton used the theory to describe the Moon's orbit around the Earth in light of the gravitational forces being exerted by the Moon, Earth and the sun. (eurekalert.org)

It could be an asymptotically periodic orbit if it converges to a periodic orbit. (wikipedia.org)

We've gotten used to planets having orbits of a few days," Winn says. (sciencedaily.com)
Like our solar system, the planets around Gliese 581 have nearly circular orbits. (scienceblog.com)

We construct graphs and corresponding initial conditions whose trajectories are periodic with an arbitrary minimal period length. (aimsciences.org)

But there are other periodic stellar phenomena that can affect light emission, such as a star eclipsing another star. (sciencedaily.com)

Orbital and adnexal involvement may involve the lacrimal gland, the eyelid, the orbit, and the lacrimal sac. (medscape.com)
The data from the dosimetry articles allowed for estimates of equivalent dose rate for 14 locations in low Earth orbit (LEO) defined by orbital inclination, altitude, and spacecraft. (cdc.gov)

Because of its size and configuration of highly reflective solar panels, the space station is now, by far, the brightest man-made object currently in orbit around the Earth. (space.com)

So for example, if a function has periodic points of order six, it has periodic points of every order other than possibly three. (stackexchange.com)
It got me wondering, what periodic points are possible in a 2-adic isometry? (stackexchange.com)
Wandering set Phase space method Cobweb plot or Verhulst diagram Periodic points of complex quadratic mappings and multiplier of orbit Orbit portrait Hale, Jack K. (wikipedia.org)
A periodic orbit is called a limit cycle if there is a neighborhood of it such that it is the \(\alpha-\)limit set or \(\omega-\)limit set of all points in the neighborhood. (scholarpedia.org)
If the maps are noninvertible, \(h\) maps forward orbits of \(f\) onto the corresponding forward orbits of \(g\ ,\) preserving the order of points. (scholarpedia.org)

Note that the problem is trivial for \(n=1\ :\) a linear system may have periodic orbits but has no limit cycle. (scholarpedia.org)

Because low statistical power, insufficient dose, insufficient latency, and exposure misclassification may be masking a relationship between ionizing radiation and mortality risk, it is advised that periodic follow-ups be performed, especially among astronauts with the largest total doses. (cdc.gov)
Goals of the SEER Program Assembling and reporting, on a periodic basis, estimates of cancer inci- dence and mortality in the United States. (cdc.gov)

This paper is concerned with formation acquisition and reconfiguration problems with an eccentric reference orbit. (elsevierpure.com)
Based on these periodic relative orbits, formation acquisition and reconfiguration problems by a feedback controller are formulated. (elsevierpure.com)

global branches of periodic orbits. (researchgate.net)

and for holomorphic dynamical systems, the orbits are Riemann surfaces. (wikipedia.org)

Nonexistence of Periodic Orbits for Predator-Prey System with Strong A" by Jinfeng Wang, Junping Shi et al. (wm.edu)
Then the inertial orbit of the follower is rotated successively around the two axes of its perifocal reference system, and the initial conditions of all noncoplanar relative orbits are derived. (elsevierpure.com)
Any nontrivial periodic solution of the system determines a closed curve on the phase plane, called a periodic orbit. (scholarpedia.org)

What makes the prospective upcoming passages so interesting is that you'll be able to see the two largest orbiting space vehicles in the sky at the same time, or within several minutes of each other. (space.com)

Are there periodic orbits of two-adic isometries not having period a power of two? (stackexchange.com)

An orbit which consists of a single point is called constant orbit. (wikipedia.org)
The orbit of an equilibrium point is a constant orbit. (wikipedia.org)

It is often the case that the evolution function can be understood to compose the elements of a group, in which case the group-theoretic orbits of the group action are the same thing as the dynamical orbits. (wikipedia.org)

The shuttle flew around the space station before finally pulling away from the orbiting laboratory, although Discovery should still remain at a relatively close distance to the station until the scheduled landing at the Kennedy Space Center in Florida on Wednesday, March 9 at 11:57 a.m. (space.com)

It tends to weakly attracting fixed point with multiplier=0.99993612384259 critical orbit tends to weakly attracting point. (wikipedia.org)

Anatomy33

Organisms6

Diseases99

Chemicals and Drugs11

Analytical, Diagnostic and Therapeutic Techniques and Equipment39

Psychiatry and Psychology5

Phenomena and Processes37

Disciplines and Occupations4

Anthropology, Education, Sociology and Social Phenomena1

Technology, Industry, Agriculture4

Information Science8

Named Groups2

Health Care13

Mathematics2

Stability10

Planar3

Dynamics2

Unstable4

Chaotic5

Arbitrarily2

Numerics1

Nonlinear equations1

Behavior4

Display periodic1

Hyperbolic2

Satellites3

Existence3

Physics3

Dynamical system2

Equations2

Dulac1

Numerical methods1

Topological2

Algebraic1

Determination1

Exhibit3

Stable2

Manifolds2

Parameters2

Classification1

Gravitational1

Asymptotically1

Planets2

Arbitrary1

Phenomena1

Orbital2

Earth1

Points5

Trivial1

Mortality2

Problems2

Global1

Systems1

System3

Time1

Period1

Constant2

Case1

Center1

Point1