Symmetry reduction and reconstruction in contact geometry and Lagrange-Poincar\'e-Herglotz equations

In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the so-called Lagrange-Poincare-Herglotz equations. Our framework relied on the associated Herglotz vector field and its projected vector field, and the use of well-chosen quasi-velocities. Some examples are also discussed.