Joseph Klein
On variational second order differential equations; polynomial case
Abstract: A general study devoted to the inverse problem of the calculus
of variations is applied to second order differential equations
$\ddot x^k=F^k(x^r,\dot x^r)$, where the $F^k$'s are polynoms of
degree two in $\dot x^r$, and conditions are given for the existence
of a Lagrangian which is itself a polynom of degree two in $\dot x^r$.
Keywords: Geom. of sec. order diff. eq.; calculus of variations.
MS classification: 34A55, 70H35.