A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

1978 ◽  
Vol 45 (3) ◽  
pp. 657-663 ◽  
Author(s):  
H. B. Hablani ◽  
S. K. Shrivastava
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Comparative Study ◽  
Density Function ◽  
Orbital Plane ◽  
Hybrid Dynamical Systems ◽  
Stability Criteria ◽  
Liapunov Stability ◽  
Dynamic Potential ◽  
The Stability

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.

scholarly journals Parameters Estimation and Stability Analysis of Nonlinear Fractional-Order Economic System Based on Empirical Data

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei He ◽  
Xiong Wang
Keyword(s):  
Genetic Algorithm ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Fractional Derivative ◽  
Empirical Data ◽  
Parameters Estimation ◽  
Stability Criteria ◽  
The Us ◽  
Novel Method ◽  
The Stability

This paper is devoted to propose a novel method for studying the macroeconomic system with fractional derivative, which can depict the memory property of actual data of economic variables. First of all, we construct a constrained optimal problem to evaluate the coefficients of nonlinear fractional financial system based on empirical data and design the corresponding genetic algorithm. Then, based on the stability criteria of fractional dynamical systems, the methodology of stability analysis is proposed to investigate the stability of the estimated nonlinear fractional dynamic system. Finally, our method is applied to discuss the macroeconomic system of the US, Australia, and UK to demonstrate its effectiveness and applicability.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

Stability Criteria and Analysis of a Monocolumn Concept

2004 ◽  
Author(s):  
Felipe Cruz Rodrigues de Campos ◽  
Marcos Cueva ◽  
Kazuo Nishimoto ◽  
Ana Paula Dos Santos Costa
Keyword(s):  
Stability Analysis ◽  
Offshore Structures ◽  
Oil Fields ◽  
Stability Criteria ◽  
Offshore Drilling ◽  
Steel Catenary Risers ◽  
Special Concern ◽  
The Stability ◽  
Almost All ◽  
Classification Society

To be classified and approved by a classification society, all offshore structures shall be submitted and analyzed according to standard rules. The stability criteria are based on the IMO–MODU (International Maritime Organization–Mobile Offshore Drilling Units) Code which has reference to almost all types of floating units such as surface, column-stabilized and self elevating, but problems were found when dealing with monocolumn concept due to differences between this concept and those presented by the rules. The monocolumn studied is a floating production system (FPS) platform designed to handle steel catenary risers (SCR) in a depth of 1800 m in Brazilian oil fields. In this project, special concern was given to sea keeping behavior, constructability and security. This paper discusses the last item, focusing on subdivision and stability analysis. In order to overcome difficulties in finding the appropriate criteria, the work was developed using a special criteria, discussed with Det Norske Veritas (DNV) and PETROBRAS, which could be implanted in future classifications for this type of hull.

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