Geometry of sprays. Lagrangian case. Principle of least curvature. (English) Zbl 0566.58012

Klein, J.

Modern developments in analytical mechanics, Vol. I: Geometrical dynamics, Proc. IUTAM-ISIMM Symp., Torino/Italy 1982, 177-196 (1983).

[For the entire collection see Zbl 0559.00013.]
From the introduction: ”In Section 1 we recall some more or less classical notions concerning vector-forms, the structure of the tangent space and connections on a vector bundle. Section 2 is devoted to the geometry of second order differential equations (semi-sprays or sprays). In Section 3 we study the special geometry of sprays defined by a Lagrangian and we give a new approach to the inverse problem of the calculus of variations. Section 4 deals with nonholonomic constraints and gives a new proof of the ”principle” of least curvature.”

Reviewer: V.Perlick

MSC:

37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H30	Other variational principles in mechanics
70H03	Lagrange’s equations

Keywords:

second order differential equations; semi-sprays; nonholonomic constraints; ”principle” of least curvature