| Contents |
| The Virial's theorem is revisited from a modern geometric perspective by making use of the symplectic formalism as an approach, both in the case of Hamiltonian and Lagrangian
systems. The particular case of Lagrangians of mechanical type will be examined and homothetic vector fields in the Riemann base manifold are related with some Virial-like theorems. It is also proved that the theory can be extended to the framework of mechanics on Lie algebroids. Several applications of the theory will be shown. |
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