Abstract
We have developed a gauge invariant approach to study the dynamical behaviour of Lagrangian systems whose potential depends on both coordinates and velocities (possibly, on time), using a geometrical description. The manifold in which the dynamical systems live is a Finslerian space in which the conformai factor is a positively homogeneous function of first degree in the velocities (the homogeneous Lagrangian of the system). This method is a generalization of the standard geometrodynamical ones which use a Riemannian manifold (see also [11]), as it permits to study a wider class of dynamical systems. Moreover, it is well suited to treat conservative systems with few degrees of freedom and peculiar dynamical systems whose Lagrangian is not ”standard”, such as the one describing the so-called Mixmaster Universe.
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