A Simplified Stability Criterion for Nonconservative Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 423-426 ◽  
Author(s):  
I. Fawzy
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Necessary Condition ◽  
Matrix Methods ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Sufficient And Necessary Condition

Dynamic stability of a general nonconservative system of n degrees of freedom is investigated. A sufficient and necessary condition for the stability of such a system is developed. It represents a simplified criterion based on the famous Lyapunov’s theorem which is proved afresh using λ-matrix methods only. When this criterion is adopted, it reduces the number of equations in Lyapunov’s method to less than half. A systematic procedure is then suggested for the stability investigation and its use is illustrated through a numerical example at the end of the paper.

Consensus Problem of Singular Multi-Agent Systems with Continuous-Time and Fixed Topology

2013 ◽  
Vol 278-280 ◽  
pp. 1687-1691
Author(s):  
Tong Qiang Jiang ◽  
Jia Wei He ◽  
Yan Ping Gao
Keyword(s):  
Continuous Time ◽  
Spanning Tree ◽  
Undirected Graph ◽  
Necessary Condition ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Fixed Topology ◽  
The Stability ◽  
Sufficient And Necessary Condition

The consensus problems of two situations for singular multi-agent systems with fixed topology are discussed: directed graph without spanning tree and the disconnected undirected graph. A sufficient and necessary condition is obtained by applying the stability theory and the system is reachable asymptotically. But for normal systems, this can’t occur in upper two situations. Finally a simulation example is provided to verify the effectiveness of our theoretical result.

Coning motion stability of spinning missiles with strapdown seekers

2016 ◽  
Vol 120 (1232) ◽  
pp. 1566-1577 ◽  
Author(s):  
S. He ◽  
D. Lin ◽  
J. Wang
Keyword(s):  
Stability Analysis ◽  
Scaling Factor ◽  
Guidance System ◽  
Necessary Condition ◽  
Stability Conditions ◽  
Motion Stability ◽  
Model Derivation ◽  
The Stability ◽  
Stability Issues ◽  
Sufficient And Necessary Condition

ABSTRACTThis paper investigates the problem of coning motion stability of spinning missiles equipped with strapdown seekers. During model derivation, it is found that the scaling factor error between the strapdown seeker and the onboard gyro introduces an undesired parasitic loop in the guidance system and, therefore, results in stability issues. Through stability analysis, a sufficient and necessary condition for the stability of spinning missiles with strapdown seekers is proposed analytically. Theoretical and numerical results reveal that the scaling factor error, spinning rate and navigation ratio play important roles in stable regions of the guidance system. Consequently, autopilot gains must be checked carefully to satisfy the stability conditions.

scholarly journals Investigation of the dynamic stability of bending-torsional deformations of the pipeline

2021 ◽  
Vol 23 (1) ◽  
pp. 72-81
Author(s):  
Petr A. Velmisov ◽  
Yuliya A. Tamarova ◽  
Yuliya V. Pokladova
Keyword(s):  
Dynamic Stability ◽  
Degrees Of Freedom ◽  
Deformable Body ◽  
Nonlinear Partial Differential Equations ◽  
Bending Moment ◽  
The Body ◽  
Initial Moment ◽  
Torsional Vibrations ◽  
Small Deviations ◽  
The Stability

Nonlinear mathematical models are proposed that describe the dynamics of a pipeline with a fluid flowing in it: a) the model of bending-torsional vibrations with two degrees of freedom; b) the model describing flexural-torsional vibrations taking into account the nonlinearity of the bending moment and centrifugal force; c) the model that takes into account joint longitudinal, bending (transverse) and torsional vibrations. All proposed models are described by nonlinear partial differential equations for unknown strain functions. To describe the dynamics of a pipeline, the nonlinear theory of a rigid deformable body is used, which takes into account the transverse, tangential and longitudinal deformations of the pipeline. The dynamic stability of bending-torsional and longitudinal-flexural-torsional vibrations of the pipeline is investigated. The definitions of the stability of a deformable body adopted in this work correspond to the Lyapunov concept of stability of dynamical systems. The problem of studying dynamic stability, namely, stability according to initial data, is formulated as follows: at what values of the parameters characterizing the gas-body system, small deviations of the body from the equilibrium position at the initial moment of time will correspond to small deviations and at any moment of time. For the proposed models, positive definite functionals of the Lyapunov type are constructed, on the basis of which the dynamic stability of the pipeline is investigated. Sufficient stability conditions are obtained that impose restrictions on the parameters of a mechanical system.

A Design Analysis Approach for Improving the Stability of Dynamic Systems with Application to the Design of Car-Trailer Systems

2005 ◽  
Vol 11 (12) ◽  
pp. 1487-1509 ◽  
Author(s):  
Y. He ◽  
H. Elmaraghy ◽  
W. Elmaraghy
Keyword(s):  
Dynamic Systems ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Integrated Approach ◽  
Design Analysis ◽  
Analysis Approach ◽  
Dynamic Mode ◽  
Stability Characteristic ◽  
Design Variables ◽  
The Stability

A design analysis approach is developed for improving the stability of dynamic systems subject to non-conservative forces. It combines genetic algorithms, sequential quadratic programming (SQP), and dynamic mode tracking (DMT). The proposed approach automatically optimizes the stability criterion and is applicable to rotor dynamics, wind turbine dynamics, aeronautics, and ground vehicle dynamics. The Routh-Hurwitz criterion has traditionally been used for determining the stability characteristics of these dynamic systems. In the conventional trial and error approaches, designers iteratively change the values of the design variables and reanalyze until an acceptable stability characteristic is achieved. This is both time-consuming and tedious. The proposed approach automates the design/analysis cycle by using the DMT technique to identify the modes; then, the SQP algorithm determines the stability criterion; and finally a genetic algorithm is applied to optimize design variables. The proposed integrated approach has been tested and evaluated numerically using a linearized car-trailer model with three degrees of freedom and the results demonstrate its feasibility and efficacy. The performed parametric sensitivity analysis revealed that the geometric parameters have a much greater influence on the lateral stability of the vehicle systems, compared with inertia parameters and torsional spring stiffness coefficients.

scholarly journals Hierarchical B-spline complexes of discrete differential forms

2018 ◽  
Vol 40 (1) ◽  
pp. 422-473 ◽  
Author(s):  
John A Evans ◽  
Michael A Scott ◽  
Kendrick M Shepherd ◽  
Derek C Thomas ◽  
Rafael Vázquez Hernández
Keyword(s):  
Stokes Problem ◽  
Differential Forms ◽  
Spatial Dimension ◽  
Necessary Condition ◽  
Two Dimensional ◽  
B Spline ◽  
Discrete Differential Forms ◽  
The Stability ◽  
Local Exactness ◽  
Sufficient And Necessary Condition

Abstract In this paper we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in electromagnetics and fluid mechanics. We derive a sufficient and necessary condition guaranteeing exactness of the hierarchical B-spline complex for arbitrary spatial dimension, and we derive a set of local, easy-to-compute and sufficient exactness conditions for the two-dimensional setting. We examine the stability properties of the hierarchical B-spline complex, and we find that it yields stable approximations of both the Maxwell eigenproblem and Stokes problem provided that the local exactness conditions are satisfied. We conclude by providing numerical results showing the promise of the hierarchical B-spline complex in an adaptive isogeometric solution framework.

scholarly journals Stability Criterion for Dynamic Gaits of Quadruped Robot

2018 ◽  
Vol 8 (12) ◽  
pp. 2381 ◽  
Author(s):  
Yan Jia ◽  
Xiao Luo ◽  
Baoling Han ◽  
Guanhao Liang ◽  
Jiaheng Zhao ◽  
...  
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Quadruped Robot ◽  
Stability Criteria ◽  
Irregular Terrain ◽  
Quadruped Robots ◽  
Simulation Results ◽  
Zero Moment ◽  
The Stability ◽  
Dynamic Gait

Dynamic-stability criteria are crucial for robot’s motion planning and balance recovery. Nevertheless, few studies focus on the motion stability of quadruped robots with dynamic gait, none of which have accurately evaluated the robots’ stability. To fill the gaps in this field, this paper presents a new stability criterion for the motion of quadruped robots with dynamic gaits running over irregular terrain. The traditional zero-moment point (ZMP) is improved to analyze the motion on irregular terrain precisely for dynamic gaits. A dynamic-stability criterion and measurement are proposed to determine the stability state of the robot and to evaluate its stability. The simulation results show the limitations of the existing stability criteria for dynamic gaits and indicate that the criterion proposed in this paper can accurately and efficiently evaluate the stability of a quadruped robot using such gaits.

On the Sufficiency of the Energy Criterion for the Stability of Certain Nonconservative Systems of the Follower-Load Type

1972 ◽  
Vol 39 (3) ◽  
pp. 717-722 ◽  
Author(s):  
H. H. E. Leipholz
Keyword(s):  
Lower Bound ◽  
Critical Load ◽  
Energy Criterion ◽  
Conservative System ◽  
Buckling Load ◽  
Follower Load ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
Divergence Type ◽  
The Stability

Using Galerkin’s method it is shown that in the domain of divergence, the nonconservative system of the follower-load type is always more stable than the corresponding conservative system. Hence, for nonconservative systems of the divergence type, the critical load of the corresponding conservative system becomes a lower bound for the buckling load, and the energy criterion remains sufficient for predicting stability. Moreover, it is proven that even for more general nonconservative systems, the energy criterion is sufficient under certain restrictions.

scholarly journals Equicontinuous geodesic flows

2009 ◽  
Vol 29 (6) ◽  
pp. 1951-1963
Author(s):  
CHRISTIAN PRIES
Keyword(s):  
Geodesic Flow ◽  
Chaotic Behavior ◽  
Conjugate Points ◽  
Necessary Condition ◽  
Riemannian Surface ◽  
Geodesic Flows ◽  
Higher Dimensional ◽  
The Stability ◽  
Flows On Surfaces ◽  
Sufficient And Necessary Condition

AbstractThis article is about the interplay between topological dynamics and differential geometry. One could ask how much information about the geometry is carried in the dynamics of the geodesic flow. It was proved in Paternain [Expansive geodesic flows on surfaces. Ergod. Th. & Dynam. Sys.13 (1993), 153–165] that an expansive geodesic flow on a surface implies that there exist no conjugate points. Instead of considering concepts that relate to chaotic behavior (such as expansiveness), we focus on notions for describing the stability of orbits in dynamical systems, specifically, equicontinuity and distality. In this paper we give a new sufficient and necessary condition for a compact Riemannian surface to have all geodesics closed; this is the idea of a P-manifold: (M,g) is a P-manifold if and only if the geodesic flow SM×ℝ→SM is equicontinuous. We also prove a weaker theorem for flows on manifolds of dimension three. Finally, we discuss some properties of equicontinuous geodesic flows on non-compact surfaces and on higher-dimensional manifolds.

scholarly journals Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yuefang Lian ◽  
Jinchuan Zhou ◽  
Jingyong Tang ◽  
Zhongfeng Sun
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Necessary Condition ◽  
Sensing Matrix ◽  
Quadratic Constraint ◽  
Linear Equality ◽  
Equality And Inequality Constraints ◽  
Measurement Vector ◽  
The Stability ◽  
Sufficient And Necessary Condition

1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.

scholarly journals Sharkovskii's order and the stability of periodic points of maps of the interval

2000 ◽  
Vol 68 (2) ◽  
pp. 244-251 ◽  
Author(s):  
Guang Yuan Zhang ◽  
Qing Zhong Li
Keyword(s):  
Positive Integer ◽  
Periodic Points ◽  
Necessary Condition ◽  
The Stability ◽  
Sufficient And Necessary Condition

AbstractLet f be a Cr (r ≥ 0) map from the interval [0, 1] into itself and m be a positive integer. This paper gives a sufficient and necessary condition under which the set of periodic points of period m disappears after a certain small Cr-perturbation.

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