On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative

2012/06/04 by Vadim V. Shurygin, Vadim V. Shurygin Jr, Shurygin, Vadim V.
Engineering · Mathematics · #34C14 #53A55 #Adhesion, Friction, and Surface Interactions #Brake Systems and Friction Analysis #Differential Equations and Numerical Methods #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:34C14 #msc:53A55

paper · pdf · doi:10.48550/arxiv.1206.0581

10 pages

openalex publication_date 2012/06/04 · arxiv created 2013/02/25 · arxiv updated 2013/02/26 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form y"²+A(x,y,y') y"+B(x,y,y')=0 to be equivalent under the action of the pseudogroup of contact transformations. These conditions are formulated in terms of integrals of some one-dimensional distributions.

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