First Order Fuzzy Dynamic Equations

2021 ◽  
pp. 137-203
Author(s):  
Svetlin G. Georgiev
Keyword(s):  
Dynamic Equations ◽  
First Order

scholarly journals Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

2018 ◽  
Vol 51 (1) ◽  
pp. 198-210 ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Ulam Stability ◽  
Step Size ◽  
First Order ◽  
Linear Dynamic ◽  
Discrete Step ◽  
Special Cases ◽  
Parameter Values ◽  
Homogeneous Linear

Abstract We establish theHyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.

scholarly journals Monotone Iterative Technique for Partial Dynamic Equations of First Order on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguang Wang ◽  
Ping Li
Keyword(s):  
Time Scales ◽  
Monotone Iterative Technique ◽  
Dynamic Equations ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Comparison Results

This work is concerned with the monotone iterative technique for partial dynamic equations of first order on time scales and for this purpose, the existence, uniqueness, and comparison results are also established.

Rotor Dynamics of Flywheel Energy Storage Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 11-18 ◽  
Author(s):  
C. P. Jayaraman ◽  
J. A. Kirk ◽  
D. K. Anand ◽  
M. Anjanappa
Keyword(s):  
Control Systems ◽  
Degrees Of Freedom ◽  
Magnetic Bearing ◽  
System Stability ◽  
Dynamic Equations ◽  
Dynamic Coupling ◽  
First Order ◽  
Torque Response ◽  
Resonance Frequencies ◽  
Computer Simulation Program

This paper deals with the dynamic analysis of the magnetic bearing stack system. The stack consists of a single flywheel supported by two magnetic bearings. To model the system, the dynamic equations of a magnetically suspended flywheel are derived. Next, the four control systems controlling the four degrees-of-freedom of the stack are incorporated into the model. The resulting dynamic equations are represented as first-order differential equations in a matrix form. A computer simulation program was then used to simulate the working of the magnetic bearing stack. Real time plots from the simulation are used to show the effect of dynamic coupling on torque response. Frequency response is used to determine the resonance frequencies of the stack system. It is found that system stability depends on flywheel speed. On the basis of the above results suggestions are made to improve stability and allow the stack to be spun beyond 60,000 rpm.

Research on Dynamics of a Three-DOF Parallel Manipulator for Levelling Mechanism

2013 ◽  
Vol 774-776 ◽  
pp. 1369-1374 ◽  
Author(s):  
Hong Jun Yang
Keyword(s):  
Parallel Manipulator ◽  
Coefficient Matrix ◽  
Dynamics Simulation ◽  
Dynamic Equations ◽  
Control System Design ◽  
Influence Coefficient ◽  
Lagrange Method ◽  
First Order ◽  
Influence Coefficient Method ◽  
Coefficient Method

A three-DOF parallel manipulator with two rotations and one translation was put forward as a levelling mechanism in this paper. Its structure and kinematics were analyzed and the first-order influence coefficient matrix was obtained by using the influence coefficient method. Then the complete and concise dynamic equations without too many unknowns were established based on Lagrange method. In addition, the dynamics simulation was carried out and the result shows that drive forces of the legs have no strong coupling, which is important to control system design.

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