scholarly journals Oscillations in a second-order discontinuous system with delay

2002 ◽  
Vol 9 (2) ◽  
pp. 339-358 ◽  
Author(s):  
Leonid Fridman ◽  
Emilia Fridman ◽  
Eugenii Shustin
2016 ◽  
Vol 26 (13) ◽  
pp. 1650224 ◽  
Author(s):  
Liping Li ◽  
Albert C. J. Luo

This paper develops the analytical conditions for the onset and disappearance of motion passability and sliding along an elliptic boundary in a second-order discontinuous system. A periodically forced system, described by two different linear subsystems, is considered mainly to demonstrate the methodology. The passable, sliding and grazing conditions of a flow to the elliptic boundary in the discontinuous dynamical system are provided through the analysis of the corresponding vector fields and [Formula: see text]-functions. Moreover, by constructing appropriate generic mappings, periodic orbits in such a discontinuous system are predicted analytically. Finally, three different cases are discussed to illustrate the existence of periodic orbits with passable and/or sliding flows. The results obtained in this paper can be applied to the sliding mode control in discontinuous dynamical systems.


Author(s):  
W. L. Bell

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.


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