The generalized Lagrangian mechanical systems

A generalized Lagrangian mechanics is a triple $\Sigma_{GL}=(M,\mathcal E,F_e)$ formed by a real $n$-dimensional manifold $M$, the generalized kinetic energy $\mathcal E$ and the external forces $F_e$. The Lagrange equations (or fundamental equations) can be defined for a generalized Lagrangian mechanical system $\Sigma_{GL}$. We get a straightforward extension of the notions of Riemannian, or Finslerian, or Lagrangian mechanical systems studied in the recent book [7]. The applications of this systems in Mechanics, Physical Fields or Relativistic Optics are pointed out. Much more information can be found in the books or papers from References [1–10].