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