Examples from the calculus of variations. I. Nondegenerate problems

Chrastina, Jan. "Examples from the calculus of variations. I. Nondegenerate problems." Mathematica Bohemica 125.1 (2000): 55-76. <http://eudml.org/doc/248651>.

@article{Chrastina2000,
abstract = {The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling the common Euler-Lagrange, Legendre, Jacobi, and Hilbert-Weierstrass conditions whenever possible and to discuss some modifications necessary in the degenerate case. The inverse and the realization problems are mentioned, too.},
author = {Chrastina, Jan},
journal = {Mathematica Bohemica},
keywords = {variational integral; critical curve; adjoint module; initial form; Poincaré-Cartan form; Lagrange problem; Mayer field; Weierstrass function; diffiety; variational integral; critical curve; adjoint module; initial form; Poincaré-Cartan form; Lagrange problem; Mayer field; Weierstrass function},
language = {eng},
number = {1},
pages = {55-76},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Examples from the calculus of variations. I. Nondegenerate problems},
url = {http://eudml.org/doc/248651},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Chrastina, Jan
TI - Examples from the calculus of variations. I. Nondegenerate problems
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 1
SP - 55
EP - 76
AB - The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling the common Euler-Lagrange, Legendre, Jacobi, and Hilbert-Weierstrass conditions whenever possible and to discuss some modifications necessary in the degenerate case. The inverse and the realization problems are mentioned, too.
LA - eng
KW - variational integral; critical curve; adjoint module; initial form; Poincaré-Cartan form; Lagrange problem; Mayer field; Weierstrass function; diffiety; variational integral; critical curve; adjoint module; initial form; Poincaré-Cartan form; Lagrange problem; Mayer field; Weierstrass function
UR - http://eudml.org/doc/248651
ER -