On the Mayer problem. II. Examples

Rok, strany: 2002, 571 - 590

Given an underdetermined system of ordinary differential equations, extremals of all possible variational problems relevant to the system together with the corresponding Poincaré-Cartan forms were characterized in geometrical terms in previous Part I of this article. The present Part II demonstrates the utility of this approach: it enables a deep insight into the structure of Euler-Lagrange and Hamilton-Jacobi equations not available by other methods and provides the sufficient extremality conditions without uncertain multipliers simi lar to the common Hilbert-Weierstrass theory. Degenerate variational problems are in principle not excluded and, like in the ``royal road'' by Carathéodory, no subtle investigation of admissible variations satisfying the boundary conditions is needed.

ISO 690:

Chrastinová, V., Tryhuk, V. 2002. On the Mayer problem. II. Examples. In Mathematica Slovaca, vol. 52, no.5, pp. 571-590. 0139-9918.

APA:

Chrastinová, V., Tryhuk, V. (2002). On the Mayer problem. II. Examples. Mathematica Slovaca, 52(5), 571-590. 0139-9918.