An Optimal Method of Solving Differential Equations Characterizing the Dynamics of a Current Collection System for an Electric Locomotive

1980 ◽  
Vol 25 (4) ◽  
pp. 329-342 ◽  
Author(s):  
GANTI PRASADA RAO ◽  
T. SRINIVASAN

The motion of an overhead trolley wire, suspended at equal intervals by stiff springs, in response to a pantograph moving with constant speed is analysed. The pantograph is modelled by two discrete masses connected by springs and dampers. Away from the supports the inertia and elasticity of the pantograph can be neglected and a simple solution for the wire and pantograph displacement is obtained. Near a support this solution is not valid as it predicts discontinuities in the vertical pantograph velocity. A different first approximation is then required in which the support elasticity and the pantograph inertia and elasticity must be included. This problem is reduced to that of solving a system of four linear differential equations containing one term with a stretched argument. The numerical and asymptotic solution of such a system is discussed and results are obtained for the contact force and pantograph displacement near a support in typical operating conditions. This disturbance at the support is propagated with the wire wave speed and reflected at the subsequent support, thus interacting with the pantograph again. This interaction is analysed and a uniformly valid solution obtained for the contact force over a complete span. Some conclusions are made about possible operating conditions in which loss of contact between the pantograph and the wire may occur.


2018 ◽  
Vol 3 (1) ◽  
pp. 65-78
Author(s):  
Elizabeth P Weinzierl ◽  
Cindy Brawley ◽  
James L Adams ◽  
Beverly B Rogers

Abstract Background Preanalytical, analytical, and postanalytical issues are often magnified in pediatric laboratories, and traditional vacuum-based blood tubes can contribute to some of these issues. Because of this, we investigated adopting an enclosed blood collection system that can perform vacuum or gentle aspiration blood collection, eliminating syringes, transfer device, and transfer steps, as well as potentially minimizing preanalytical error in the pediatric laboratory. We embarked on a validation of this tube system, in comparison with our current collection tubes, across most in-house tests at a large pediatric hospital. Methods Twenty adult volunteers were recruited. Blood was drawn into lithium heparin, serum, EDTA, and citrate tubes of each commercial tube type for comparison. For some tests, remnant blood from pediatric syringe draws was used when available. Samples were then processed and analyzed across all general areas of the clinical laboratory, and correlations of the results from the 2 tube systems were performed. Results Across 95 tests in the core laboratory and blood bank, almost all demonstrated clinically acceptable comparisons, with most R values >0.90. Only 3 of 95 tests demonstrated clinically significant differences between the tube systems. Conclusions Our validation of the enclosed blood collection system demonstrated acceptable results when compared with our current collection tubes. Additionally, with some minor modifications, our automated instruments could utilize ultralow-volume tubes from the enclosed blood collection system for direct tube sampling, which is impossible using our current small-volume tubes with our main chemistry analyzer.


2020 ◽  
Author(s):  
Hafida Laib ◽  
Azzeddine Bellour ◽  
Aissa Boulmerka

Abstract The present paper deals with the numerical solution for a general form of a system of nonlinear Volterra delay integro-differential equations (VDIDEs). The main purpose of this work is to provide a current numerical method based on the use of continuous collocation Taylor polynomials for the numerical solution of nonlinear VDIDEs systems. It is shown that this method is convergent. Numerical results will be presented to prove the validity and effectiveness of this convergent algorithm. We apply two models to the COVID-19 epidemic in China and one for the Predator-Prey model in mathematical ecology.


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