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On the Mayer problem. I. General principles

In: Mathematica Slovaca, vol. 52, no. 5
Veronika Chrastinová - Václav Tryhuk

Details:

Year, pages: 2002, 555 - 570
About article:
Given an underdetermined system of ordinary differential equations (i.e., the Monge system, the optimal control system) expressed by Pfaffian equations $ω\equiv 0$ ($ω\inΩ$) where $Ω$ is a module of differential $1$@-forms on a space $M$, we determine submodules $\breveΩ\subsetΩ$ which satisfy the congruence $d \breveΩ\simeq 0$ $\pmod {\breveΩ, Ω\wedgeΩ}$ along a certain special subspace $E\subsetM$ of the total space $M$. Then $\breveΩ$ and $E$ may be interpreted in terms of Poincaré-Cartan forms and Euler-Lagrange equations for various Mayer problems that belong to the given Monge system. They yield a universal canonical formalism including the Weierstrass-Hilbert extremality theory. The occurrences of uncertain coefficients (Lagrange multipliers, adjoint variables) are suppressed and occasionally eliminated (e.g., for all Mayer problems arising from a Lagrange problem), the degenerate cases are not excluded.
How to cite:
ISO 690:
Chrastinová, V., Tryhuk, V. 2002. On the Mayer problem. I. General principles. In Mathematica Slovaca, vol. 52, no.5, pp. 555-570. 0139-9918.

APA:
Chrastinová, V., Tryhuk, V. (2002). On the Mayer problem. I. General principles. Mathematica Slovaca, 52(5), 555-570. 0139-9918.