On the Stability of the rotation under the action of constant momentum Lagrangian top with perfect fluid in a resisting medium

2019 ◽  
Vol 33 ◽  
pp. 122-131
Author(s):  
Yuri Kononov ◽  
Valeriya Vasylenko
Keyword(s):  
Asymptotic Stability ◽  
Solid Body ◽  
Ideal Liquid ◽  
Uniform Rotation ◽  
Ellipsoidal Cavity ◽  
Resisting Medium ◽  
Lagrange Top ◽  
The Stability ◽  
Constant Moment ◽  
The Ideal

The rotation around a fixed point of a heavy dynamically symmetric solid body with an arbitrary asymmetric cavity completely filled with an ideal in-compressible liquid is considered. The stability of a uniform rotation of a Lagrang' top with the ideal liquid in a resisting medium under condition of a given constant moment is investigated. The equation of the perturbed motion of the Lagrang' top with the ideal liquid is presented. It is proved the follow-ing: the asymptotic stability of uniform rotation for an ellipsoidal cavity will be only for a compressed ellipsoidal cavity. It has been observed that most practically important cases consider the main effect of the ideal liquid influence on the motion of a solid can be researched by means of considering only the fundamental tone of the liquid oscillation. Conditions of uniform rotation asymptotic stability in a resistive medium under the action of the Lagrange top' constant moment with an arbitrary axisymmetric cavity containing an ideal liquid are obtained. Stability conditions are derived with provisions for the main and additional tones of liquid oscillations. The heavy solid body with the fixed-point value is ex-posed to the action of a constant moment in the inertial coordinate system. Analytic and numerical investigations of the main and additional tones of liquid oscillations influence, over-turning, restoring, dissipative and constant moments on the conditions of the asymptotic stability of the uniform rotation of the Lagrange top with an ideal liquid are carried out. It is stated the following: cubic and square inequalities presented in the paper are conditions of asymptotic stability if the basic tone of liquid fluctuations will be mentioned. Stability region numerical studies have been carried out on the example of an ellipsoidal cavity. It is presented that increasing of the equatorial moment of inertia of the solid body de-creases its stability region as well as the increasing of the solid body inertia axial moment in-creases the last one.

On the subject of influence of dissipative and constant of moments on the stability of uniform rotations of non-free two elastically connected gyroscopes of Lagrange

2021 ◽  
Vol 34 ◽  
pp. 50-61
Author(s):  
Yurii Kononov ◽  
Yaroslav Sviatenko
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Stability Conditions ◽  
Inertial Coordinate System ◽  
Resisting Medium ◽  
Angular Velocities ◽  
The Subject ◽  
The Stability ◽  
Spherical Hinge ◽  
Asymptotic Stability Conditions

The conditions for asymptotic stability of uniform rotations in a resisting medium of two heavy Lagrange gyroscopes connected by an elastic spherical hinge are obtained in the form of a system of three inequalities. The bottom gyroscope has a fixed point. The rotation of the gyroscopes is maintained by constant moments in the inertial coordinate system. The influence of the elasticity of the hinge on the stability conditions is estimated. It is shown that for a sufficiently high rigidity of the hinge, the asymptotic stability conditions are determined by only one inequality, which coincides with the inequality obtained for the case of a cylindrical hinge. When the angular velocities of the gyroscopes' own rotations coincide, this inequality coincides with the well--known condition for one gyroscope. Cases of degeneration of an elastic spherical hinge into a spherical inelastic, cylindrical and universal elastic hinge (Hooke's hinge) are considered. For the Hooke hinge, it is shown that there is no asymptotic stability at a sufficiently high angular velocity of gyroscopes rotation.

A New CRONE Suspension: More Compact and More Efficient: Part 2—Synthesis and Achievement

2009 ◽  
Author(s):  
Audrey Rizzo ◽  
Xavier Moreau ◽  
Alain Oustaloup ◽  
Vincent Hernette
Keyword(s):  
Transfer Function ◽  
Fractional Derivative ◽  
Vibration Isolation ◽  
Suspension System ◽  
Technological Parameters ◽  
Stability Degree ◽  
Parallel Arrangement ◽  
The Stability ◽  
Crone Suspension ◽  
The Ideal

In a vibration isolation context, fractional derivative can be used to design suspensions which allow to obtain similar performances in spite of parameters uncertainties. This paper presents the synthesis and the achievement of a new Hydractive CRONE suspension system. After the study of the different constraint in suspension in the first paper, the ideal transfer function of the hydractive CRONE suspension is created and simulated in different case. Then a method to determine the technological parameters is proposed. A parallel arrangement of dissipative and capacitive components and a gamma arrangement are compared. They lead to the same unusual performances: the stability degree robustness and the rapidity robustness.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

scholarly journals The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wen-Juan Wang ◽  
Yan Jia
Keyword(s):  
Weak Solution ◽  
Asymptotic Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Perturbed System ◽  
Regular Class ◽  
Stability Issue ◽  
The Stability

We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solutionuof the Navier-Stokes equations lies in the regular class∇u∈Lp(0,∞;Bq,∞0(ℝ3)),(2α/p)+(3/q)=2α,2<q<∞,0<α<1, then every weak solutionv(x,t)of the perturbed system converges asymptotically tou(x,t)asvt-utL2→0,t→∞.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

scholarly journals III. Researches in physical astronomy

1831 ◽  
Vol 121 ◽  
pp. 17-66
Keyword(s):  
Angular Velocity ◽  
Major Axis ◽  
The Body ◽  
Fixed Plane ◽  
Resisting Medium ◽  
Axis Of Rotation ◽  
Geographical Latitude ◽  
The Mean ◽  
The Stability ◽  
Revolving Body

In last April I had the honour of presenting to the Society a paper containing expressions for the variations of the elliptic constants in the theory of the motions of the planets. The stability of the solar system is established by means of these expressions, if the planets move in a space absolutely devoid of any resistance*, for it results from their form that however far the ap­proximation be carried, the eccentricity, the major axis, and the tangent of the inclination of the orbit to a fixed plane, contain only periodic inequalities, each of the three other constants, namely, the longitude of the node, the longitude of the perihelion, and the longitude of the epoch, contains a term which varies with the time, and hence the line of apsides and the line of nodes revolve continually in space. The stability of the system may therefore be inferred, which would not be the case if the eccentricity, the major axis, or the tangent of the inclination of the orbit to a fixed plane contained a term varying with the time, however slowly. The problem of the precession of the equinoxes admits of a similar solution; of the six constants which determine the position of the revolving body, and the axis of instantaneous rotation at any moment, three have only periodic inequalities, while each of the other three has a term which varies with the time. From the manner in which these constants enter into the results, the equilibrium of the system may be inferred to be stable, as in the former case. Of the constants in the latter problem, the mean angular velocity of rotation may be considered analogous to the mean motion of a planet, or its major axis ; the geographical longitude, and the cosine of the geographical latitude of the pole of the axis of instantaneous rotation, to the longitude of the perihelion and the eccentricity; the longitude of the first point of Aries and the obliquity of the ecliptic, to the longitude of the node and the inclination of the orbit to a fixed plane; and the longitude of a given line in the body revolving, passing through its centre of gravity, to the longitude of the epoch. By the stability of the system I mean that the pole of the axis of rotation has always nearly the same geographical latitude, and that the angular velocity of rotation, and the obliquity of the ecliptic vary within small limits, and periodically. These questions are considered in the paper I now have the honour of submitting to the Society. It remains to investigate the effect which is produced by the action of a resisting medium; in this case the latitude of the pole of the axis of rotation, the obliquity of the ecliptic, and the angular velocity of rotation might vary considerably, although slowly, and the climates undergo a con­siderable change.

scholarly journals Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

2012 ◽  
Vol 22 (2) ◽  
pp. 401-408 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Type Model ◽  
Stability Tests ◽  
Numerical Examples ◽  
Computer Methods ◽  
Discrete Linear Systems ◽  
Complex Functions ◽  
The Stability

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systemsAsymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

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