Examples from the calculus of variations. III. Legendre and Jacobi conditions

Jan Chrastina

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 93-111
  • ISSN: 0862-7959

Abstract

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We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.

How to cite

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Chrastina, Jan. "Examples from the calculus of variations. III. Legendre and Jacobi conditions." Mathematica Bohemica 126.1 (2001): 93-111. <http://eudml.org/doc/248828>.

@article{Chrastina2001,
abstract = {We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.},
author = {Chrastina, Jan},
journal = {Mathematica Bohemica},
keywords = {Legendre condition; Jacobi condition; Poincaré-Cartan form; Lagrange problem; degenerate variational integral; Legendre condition; Jacobi condition; Poincaré-Cartan form; Lagrange problem; degenerate variational integral},
language = {eng},
number = {1},
pages = {93-111},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Examples from the calculus of variations. III. Legendre and Jacobi conditions},
url = {http://eudml.org/doc/248828},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Chrastina, Jan
TI - Examples from the calculus of variations. III. Legendre and Jacobi conditions
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 93
EP - 111
AB - We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.
LA - eng
KW - Legendre condition; Jacobi condition; Poincaré-Cartan form; Lagrange problem; degenerate variational integral; Legendre condition; Jacobi condition; Poincaré-Cartan form; Lagrange problem; degenerate variational integral
UR - http://eudml.org/doc/248828
ER -

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