Article

 Title: Některé vlastnosti nelineárních obvodu a fyzikální význam jakobiánu (Czech) Title: Some properties of nonlinear circuits and a physical interpretation of the Jacobian (English) Author: Jiřina, Marcel Language: Czech Journal: Aplikace matematiky ISSN: 0373-6725 Volume: 18 Issue: 2 Year: 1973 Pages: 77-82 Summary lang: English Summary lang: Czech . Category: math . Summary: A practical problem leads to the investigation of a system of equations in the form $f(x,y,y',z)=0$. The well-known theorem on the solvability of the system of equations in the form $f(x,y,y',z)=0$ applies also to the above system. The condition that the Jacobian $\bold J=\partial t/\partial(y',z)$ is nonzero is, under the corresponding assumptions, sufficient for the existence of a solution $(y(x), y(x))$ of the system. Further the necessity of this condition is proved if the functions $z(x)$ and $y(x)$ are required to be respectively once and twice continuously differentiable. The presented theorem may be applied in mechanics as well as in the theory of electric circuits with concentrated parameters. () MSC: 34A12 MSC: 34C25 MSC: 94A20 MSC: 94C10 idZBL: Zbl 0255.34004 idMR: MR0316647 DOI: 10.21136/AM.1973.103453 . Date available: 2008-05-20T17:55:25Z Last updated: 2020-07-28 Stable URL: http://hdl.handle.net/10338.dmlcz/103453 . Reference: [1] Stern T. E.: Computer-aided analysis of nonlinear networks described by constrained differential equations.Proc. of International Symp. on Network Theory, Belgrade 1968, s. 179-190. Reference: [2] Ince E. L.: Ordinary Differential Equations.1927. Zbl 0612.34002 Reference: [3] Jiřina M.: Solvability of the equations of the networks with lumped general variable parameters.Information processing machines Sborník VÚMS, č. 20, 1973. Reference: [4] Jiřina M.: Řešitelnost rovnic nelineárních obvodů sestavených metodou uzlových napětí.Elektrotechnický časopis č. 1, 1972. MR 0388614 .

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