A Study of Coupled Mathieu Equations by Use of Infinite Determinants

1976 ◽  
Vol 43 (2) ◽  
pp. 349-352 ◽  
Author(s):  
Ti-Chiang Lee
Keyword(s):  
Finite Number ◽  
Numerical Results ◽  
Stability Properties ◽  
Hill’S Method ◽  
The Stability ◽  
Mathieu Equations ◽  
Stability Of The Solution

Hill’s method of infinite determinant is applied to solving a system of Mathieu-type equations. Expansion of the converging infinite determinant then leads to the criterion for stability of the solution. Numerical results are then presented in graphs for two examples. Good agreements between the present results and the existing solutions are observed. The criterion therefore is useful to predict the stability properties of a finite number of coupled Mathieu equations.

scholarly journals Dynamics of a Discretization Physiological Control System

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohua Ding ◽  
Huan Su
Keyword(s):  
Control System ◽  
Discrete System ◽  
Numerical Results ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Physiological Control ◽  
Midpoint Rule ◽  
The Stability ◽  
Stability Of The Solution

We study the dynamics of solutions of discrete physiological control system obtained by Midpoint rule. It is shown that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases and we analyze the stability of the solution of the discrete system and calculate the direction of the Hopf bifurcations. The numerical results are presented.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability

scholarly journals CONVERGENCE OF COMONOTONE HISTOPOLATING SPLINES

2015 ◽  
Vol 20 (1) ◽  
pp. 124-138 ◽  
Author(s):  
Helle Hallik ◽  
Peeter Oja
Keyword(s):  
Convergence Rate ◽  
Finite Number ◽  
Numerical Results ◽  
Quadratic Polynomial

The convergence rate of histopolation on an interval with combined splines of class C1 having linear/linear rational or quadratic polynomial pieces is studied. The function to histopolate may have finite number of derivative zeros and established convergence rate depends mainly on the behaviour of the derivative near its zeros. Given numerical results are completely consistent with theoretical ones.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

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