The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and
it is entirely solved for the differential operators, but only a few results are known in the more …

Linear connections for systems of second-order ordinary differential equations Page 1
ANNALES DE L’IHP, SECTION A M. CRAMPIN E. MARTÍNEZ W. SARLET Linear …

A geometrical framework is presented for the treatment of a class of dynamical systems,
which are modelled by a system of second-order differential equations, coupled with first …

In this essentially selfcontained paper first we establish an intrinsic version and present a
coordinate-free deduction of the so-called Rapcsák equations, which provide, in the form of …

We present several results on the inverse problem and equivalent contact Lagrangian
systems. These problems naturally lead to consider smooth transformations on the z …

The main objective of this paper is to work out a full-scale application of the integrability
analysis of the inverse problem of the calculus of variations, as developed in recent papers …

A novel approach to a coordinate-free analysis of the multiplier question in the
inverseproblem of the calculus of variations, initiated in a previous publication, is completed …

We introduce a method which allows one to recover the equations of motion of a class of
nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full …

Relations between Lagrangian structures, metric structures, and semispray connections on
a manifold are investigated. Generalized Finsler structures (called quasifinslerian) are …

This paper deals with the inverse problem of the calculus of variations for systems of second-
order ordinary differential equations. The case of the problem which Douglas, in his …