On Stability of the Mechanical Lagrangian Systems

Abstract

Abstract. It is well known that a Randers metric is a deformation of a Riemannian metric alfa(x,y)=sqrt(a_ij(x)y^iy^j)) using a 1-form beta(x,y)=beta_i(x)y^i. In this paper we are replacing beta(x,y) with beta_2(x,y)=sqrt(beta_ij(x)y^iy^j. We obtain a new space and we are going to study some of its properties.