Cantrijn, F.; Crampin, M.; Sarlet, W. Evading the inverse problem for second-order ordinary differential equations by using additional variables. (English) Zbl 0616.34008 Inverse Probl. 3, 51-63 (1987). In a recent work G. Caviglia [Int. J. Theor. Phys. 25, 139-146 (1986; Zbl 0608.34053)] has shown that any system of second order ordinary differential equations may be extended in such a way as to embed them in a system of Euler-Lagrange equations. The authors, in this paper, give a geometrical description of this construction and show how in effect the same function may be used to define both a Hamiltonian and a Lagrangian extension of the given system. They further clarify the way in which the linear variational equations and their adjoints come into the picture, and also their connection with symmetries of the system and invariant 1-forms. Reviewer: N.L.Maria Cited in 4 Documents MSC: 34A55 Inverse problems involving ordinary differential equations Keywords:second order ordinary differential; Euler-Lagrange equations; linear variational equations Citations:Zbl 0608.34053 PDFBibTeX XMLCite \textit{F. Cantrijn} et al., Inverse Probl. 3, 51--63 (1987; Zbl 0616.34008) Full Text: DOI