Bi-para-mechanical systems on the bi-Lagrangian manifold

This paper explores the generalization of some techniques introduced in the papers (see [12,13]). Clearly, mechanical systems have been studied by means of the geometry of tangent bundle, more precisely, using polynomic structures on complex- and para-complex-manifolds. Also, formalisms of Lagrangian and Hamiltonian mechanics have intrinsically been described on the bi-Lagrangian manifold. This study showed that physically working on a subdomain of a manifold has been seen to be the same as working on the manifold. © 2010 Elsevier B.V. All rights reserved