A note on dynamical systems satisfying the Wnschmann-type condition

Abstract

Dynamical systems of second order ordinary differential equations (SODEs) satisfying the Wunschmann-type condition are presented, with a special emphasis on SODEs provided by Euler-Lagrange equations, particularly, geodesics on surfaces. Some remarkable facts are to be pointed: three of our examples are of quasi Euler-Lagrange nature; also, except one example that leads to classical Euclidean 2D metric, all yields a semi-Riemannian metric. Key words: Second order ordinary differential equations (SODE), semispray-metric, Hamilton-Jacobi equation, dynamical systems, Wunschmann-type condition, (quasi) Euler-Lagrange equation, geodesic equation.