This article is cited in 2 papers

One-dimensional Lagrangians generated by a quadratic form

V. A. Luk'yanov

Zavolzhsk Branch of Nizhny Novgorod State Technical University

Abstract: In this paper we apply the classical variational calculus to the Lagrangians of particular type. Namely, we establish formulas for the 1$^\mathrm{st}$ integrals and propose a technique for obtaining invariant 1$^\mathrm{st}$ integrals. We also deduce the differential homogeneity conditions for Lagrangians with respect to multiplication of the path $x(t)$ by the function $c(t)$ and with respect to the change of the parameter $t=t(s)$.

Keywords: conformally connected manifold, Euler–Lagrange equation, integral functionals, isotropic extreme curve, one-dimensional Lagrangians, orthogonal group, path, quadratic form, scalar product.

UDC: 519.3

Received: 26.03.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:5, 28–37

Bibliographic databases:

•