International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Full Length Research Paper

A note on dynamical systems satisfying the Wünschmann-type condition

Mircea Crăşmăreanu1 and Vlad Enache2*
1Faculty of Mathematics,"Al. I. Cuza" University, Iasi, 700506, Romania 2Department of Sciences, "Al. I. Cuza" University, Iasi, 700107, Romania
Email: [email protected]

  •  Accepted: 12 February 2012
  •  Published: 30 September 2013


Dynamical systems of second order ordinary differential equations (SODEs) satisfying the Wünschmann-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, Wünschmann-type condition, (quasi) Euler-Lagrange equation, geodesic equation.