Některé vlastnosti nelineárních obvodu a fyzikální význam jakobiánu

Jiřina, Marcel

Applications of Mathematics, Tome 18 (1973) no. 2, pp. 77-82.

Résumé

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.

Détail

DOI : 10.21136/AM.1973.103453

Classification : 34A12, 34C25, 94A20, 94C10