scholarly journals Averaging Methods for Design of Spacecraft Hysteresis Damper

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ricardo Gama ◽  
Anna D. Guerman ◽  
Ana Seabra ◽  
Georgi V. Smirnov
Keyword(s):  
Differential Equations ◽  
Parameter Optimization ◽  
Numerical Optimization ◽  
Gravity Gradient ◽  
Analytic Method ◽  
Discontinuous System ◽  
Discontinuous Differential Equations ◽  
Averaging Methods ◽  
Attitude Stabilization ◽  
Averaging Techniques

This work deals with averaging methods for dynamics of attitude stabilization systems. The operation of passive gravity-gradient attitude stabilization systems involving hysteresis rods is described by discontinuous differential equations. We apply recently developed averaging techniques for discontinuous system in order to simplify its analysis and to perform parameter optimization. The results obtained using this analytic method are compared with those of numerical optimization.

Bidimensional Fluid-Film Flows of Stokesian Fluids

1982 ◽  
Vol 104 (2) ◽  
pp. 227-233
Author(s):  
Patrick Bourgin ◽  
Bernard Gay
Keyword(s):  
Laminar Flow ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Differential System ◽  
Analytic Method ◽  
Shearing Stress ◽  
Flow Equations ◽  
Approximate Analytic Method ◽  
Film Flows

The bidimensional flow equations of a Stokesian fluid are solved for the case of steady, incompressible, and laminar flow between two arbitrary moving surfaces separated by a small gap. The stress T22 and the shearing stress at one of the walls are coupled through nonlinear integro-differential equations, depending on the viscous function only. The form of this differential system is specified for the equations derived from the theory of phenomenological macrorheology, as developed by Reiner and Rivlin. The solution is proved to be unique under certain conditions and for adequate boundary conditions. An example is worked out in the particular case of one single non-Newtonian parameter. The problem is solved in two different ways, using an approximate analytic method and a numerical method. The conception of the latter allows to generalize it by introducing only slight modifications into the program.

Lyapunov Instability for Discontinuous Differential Equations

2021 ◽  
Vol 2 (2) ◽  
pp. 49-58
Author(s):  
Iguer Luis Domini dos Santos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Discontinuous Differential Equations ◽  
Lyapunov Instability

The present work studies the Lyapunov instability for discontinuous differential equations through the use of the notion of Carathéodory solution to differential equations. From Lyapunov's first instability theorem and Chetaev's instability theorem, which deal with instability to ordinary differential equations, two Lyapunov instability results for discontinuous differential equations are obtained.

On the Number of Limit Cycles of Discontinuous Liénard Polynomial Differential Systems

2018 ◽  
Vol 28 (14) ◽  
pp. 1850175
Author(s):  
Fangfang Jiang ◽  
Zhicheng Ji ◽  
Yan Wang
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Upper Bounds ◽  
Second Order ◽  
Discontinuous Differential Equations ◽  
Differential Systems ◽  
Lower Upper ◽  
First Order ◽  
Polynomial Differential Systems ◽  
Averaging Theorem

In this paper, we investigate the number of limit cycles for two classes of discontinuous Liénard polynomial perturbed differential systems. By the second-order averaging theorem of discontinuous differential equations, we provide several criteria on the lower upper bounds for the maximum number of limit cycles. The results show that the second-order averaging theorem of discontinuous differential equations can predict more limit cycles than the first-order one.

scholarly journals Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization

1999 ◽  
Vol 7 (1) ◽  
pp. 19-44 ◽  
Author(s):  
Slawomir Koziel ◽  
Zbigniew Michalewicz
Keyword(s):  
Evolutionary Algorithms ◽  
Parameter Optimization ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Search Space ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
New Approach ◽  
Survey Papers ◽  
Dimensional Cube

During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential.

scholarly journals Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

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