Některé vlastnosti nelineárních obvodu a fyzikální význam jakobiánu
Applications of Mathematics, Tome 18 (1973) no. 2, pp. 77-82
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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.
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
@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 -
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[4] Jiřina M.: Řešitelnost rovnic nelineárních obvodů sestavených metodou uzlových napětí. Elektrotechnický časopis č. 1, 1972. | MR
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