Geometrical characteristics of the stability domain in the restricted problem of eight bodies

2019 ◽  
Vol 28 (1) ◽  
pp. 49-52
Author(s):  
ELENA CEBOTARU ◽  
Keyword(s):  
Restricted Problem ◽  
Stability Domain ◽  
Stationary Solutions ◽  
Symbolic Calculation ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Calculation System ◽  
The Stability

The eight-body Newtonian problem is studied. Applying the symbolic calculation system Mathematica the stationary solutions, their stability in numerical form and the geometric characteristics of the stability domain are studied.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

2014 ◽  
Vol 31 (02) ◽  
pp. 1440002 ◽  
Author(s):  
K. AVRACHENKOV ◽  
E. MOROZOV ◽  
R. NEKRASOVA ◽  
B. STEYAERT
Keyword(s):  
Queueing System ◽  
Stability Domain ◽  
Single Server ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Single Orbit ◽  
Transmission Control Protocols ◽  
Regenerative Approach ◽  
The Stability ◽  
Multi Access

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

Analytical and Experimental Flutter Analysis of a Typical Wing Section Carrying a Flexibly Mounted Unbalanced Engine

2019 ◽  
Vol 19 (02) ◽  
pp. 1950013 ◽  
Author(s):  
A. S. Mirabbashi ◽  
A. Mazidi ◽  
M. M. Jalili
Keyword(s):  
Stability Domain ◽  
Governing Equations ◽  
Lagrange Equations ◽  
Wing Section ◽  
Unbalanced Force ◽  
Engine Thrust ◽  
Finite State Model ◽  
Flutter Analysis ◽  
Finite State ◽  
The Stability

In this paper, both experimental and analytical flutter analyses are conducted for a typical 5-degree of freedon (5DOF) wing section carrying a flexibly mounted unbalanced engine. The wing flexibility is simulated by two torsional and longitudinal springs at the wing elastic axis. One flap is attached to the wing section by a torsion spring. Also, the engine is connected to the wing by two elastic joints. Each joint is simulated by a spring and damper unit to bring the model close to reality. Both the torsional and longitudinal motions of the engine are considered in the aeroelastic governing equations derived from the Lagrange equations. Also, Peter’s finite state model is used to simulate the aerodynamic loads on the wing. Effects of various engine parameters such as position, connection stiffness, mass, thrust and unbalanced force on the flutter of the wing are investigated. The results show that the aeroelastic stability region is limited by increasing the engine mass, pylon length, engine thrust and unbalanced force. Furthermore, increasing the damping and stiffness coefficients of the engine connection enlarges the stability domain.

scholarly journals Lr-LpStability of the Incompressible Flows with Nonzero Far-Field Velocity

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Jaiok Roh
Keyword(s):  
Constant Velocity ◽  
Incompressible Flows ◽  
Temporal Stability ◽  
Stationary Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Far Field ◽  
Spatial Direction ◽  
Field Velocity ◽  
The Stability

We consider the stability of stationary solutionswfor the exterior Navier-Stokes flows with a nonzero constant velocityu∞at infinity. Foru∞=0with nonzero stationary solutionw, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability inLpspaces for1<pand obtained good stability decay rates. For the spatial direction, we recently obtained some results. Foru∞≠0, Heywood (1970, 1972) and Masuda (1975) have studied the temporal stability inL2space. Shibata (1999) and Enomoto and Shibata (2005) have studied the temporal stability inLpspaces forp≥3. Then, Bae and Roh recently improved Enomoto and Shibata's results in some sense. In this paper, we improve Bae and Roh's result in the spacesLpforp>1and obtainLr-Lpstability as Kozono and Ogawa and Borchers and Miyakawa obtained foru∞=0.

scholarly journals Stability of a Hot Smoluchowski Fluid

2001 ◽  
Vol 08 (01) ◽  
pp. 19-27 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Numerical Range ◽  
Nonlinear Parabolic Equations ◽  
Stationary Solutions ◽  
Small Perturbations ◽  
Material Density ◽  
Nonlinear Parabolic ◽  
The Stability ◽  
Special Case

We study coupled nonlinear parabolic equations for a fluid described by a material density ρ and a temperature Θ, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on the boundary, with no-escape boundary conditions for the material. For the special case, where the temperature on the boundary is the same at both ends, the linearized equations for small perturbations about a stationary solution at uniform temperature and density are derived; they are subject to boundary conditions, Dirichlet for Θ and no-flow conditions for the material. The spectrum of the generator L of time evolution, regarded as an operator on L2[0,1], is shown to be real, discrete and non-positive, even though L is not self-adjoint. This result is necessary for the stability of the stationary state, but might not be sufficient. The problem lies in the fact that L is not a sectorial operator, since its numerical range is ℂ.

Ellipsoidal approximation of the stability domain of a polynomial

2001 ◽  
Author(s):  
Didier Henrion ◽  
Dimitri Peaucelle ◽  
Denis Arzelier ◽  
Michael Sebek
Keyword(s):  
Stability Domain ◽  
Ellipsoidal Approximation ◽  
The Stability

Domains and Types of Aeroelastic Instability of Slender Beam

2007 ◽  
Author(s):  
Jirˇi´ Na´prstek
Keyword(s):  
Stability Boundary ◽  
Stability Loss ◽  
Stability Domain ◽  
Theoretical Explanation ◽  
Point Of View ◽  
System Response ◽  
Physical Point ◽  
Model Response ◽  
Gyroscopic Forces ◽  
The Stability

Slender structures exposed to a cross air flow are prone to vibrations of several types resulting from aeroelastic interaction of a flowing medium and a moving structure. Aeroelastic forces are the origin of nonconservative and gyroscopic forces influencing the stability of a system response. Conditions of a dynamic stability loss and a detailed analysis of a stability domain has been done using a linear mathematical model. Response properties of a system located on a stability boundary together with tendencies in its neighborhood are presented and interpreted from physical point of view. Results can be used for an explanation of several effects observed experimentally but remaining without theoretical explanation until now.

scholarly journals Application of computer algebra for the construction of shell models of turbulence

2019 ◽  
Vol 127 ◽  
pp. 02004
Author(s):  
Liubov Feshchenko ◽  
Gleb Vodinchar
Keyword(s):  
Conservation Laws ◽  
Computer Algebra ◽  
Nonlinear Interaction ◽  
Stationary Solutions ◽  
Symbolic Calculation ◽  
Shell Models ◽  
Model Equations ◽  
Shell Models Of Turbulence

The technique for automatic constructing of shell models of turbulence has been developed. The compilation of a model equations and its exactly solution is implemented using computer algebra (symbolic calculation) systems. The technique allows one to vary the scaling nonlocality of nonlinear interaction, form of expressions for conservation laws in models, and the form of stationary solutions with power distributions to scales.

scholarly journals On The Stability of Stationary Solutions of the Twice-Averaged Hill’s Problem Taking Into Account The Planet Oblateness

1999 ◽  
Vol 172 ◽  
pp. 457-457
Author(s):  
M.A. Vashkovyak
Keyword(s):  
Orbital Evolution ◽  
Stationary Solutions ◽  
Circular Orbits ◽  
Hill’S Problem ◽  
Hill's Problem ◽  
The Stability

The problem of satellite orbital evolution with the combined influence of a distant perturbing body and the planet oblateness is well known (Laplace, 1805; Lidov, 1962, 1973; Kozai, 1963; Kudielka, 1994, 1997). The case of near-circular orbits is investigated in more details in (Sekiguchi, 1961; Allan and Cook, 1964; Vashkovyak, 1974).

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