×

On first integrals of a system of differential equations. (Russian) Zbl 0602.34008

This paper deals with systems of ordinary differential equations of the form \(\ddot q_ i=\alpha_ i(t,q_ 1,...,q_ n,\dot q_ 1,...,\dot q_ n),\) \(i=1,2,...,n\), in which the right-hand sides are twice continuously differentiable. Assuming that a differentiable function \(f(t,q_ 1,...,q_ n,\dot q_ 1,...,\dot q_ n)\) does exist, such that \(df/dt=\partial \alpha_ k/\partial q_ k,\) \(k=1,2,...,n\), then a first integral of the system can be constructed.
Reviewer: C.Corduneanu

MSC:

34A34 Nonlinear ordinary differential equations and systems
PDFBibTeX XMLCite