Některé vlastnosti nelineárních obvodu a fyzikální význam jakobiánu
Applications of Mathematics, Tome 18 (1973) no. 2, pp. 77-82
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.
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.
@article{10_21136_AM_1973_103453,
author = {Ji\v{r}ina, Marcel},
title = {N\v{e}kter\'e vlastnosti neline\'arn{\'\i}ch obvodu a fyzik\'aln{\'\i} v\'yznam jakobi\'anu},
journal = {Applications of Mathematics},
pages = {77--82},
year = {1973},
volume = {18},
number = {2},
doi = {10.21136/AM.1973.103453},
mrnumber = {0316647},
zbl = {0255.34004},
language = {cs},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1973.103453/}
}
TY - JOUR AU - Jiřina, Marcel TI - Některé vlastnosti nelineárních obvodu a fyzikální význam jakobiánu JO - Applications of Mathematics PY - 1973 SP - 77 EP - 82 VL - 18 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1973.103453/ DO - 10.21136/AM.1973.103453 LA - cs ID - 10_21136_AM_1973_103453 ER -
Jiřina, Marcel. Některé vlastnosti nelineárních obvodu a fyzikální význam jakobiánu. Applications of Mathematics, Tome 18 (1973) no. 2, pp. 77-82. doi: 10.21136/AM.1973.103453
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[3] Jiřina M.: Solvability of the equations of the networks with lumped general variable parameters. Information processing machines Sborník VÚMS, č. 20, 1973.
[4] Jiřina M.: Řešitelnost rovnic nelineárních obvodů sestavených metodou uzlových napětí. Elektrotechnický časopis č. 1, 1972. | MR
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