Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved in classical systems. this article, a Noether's theorem for non-autonomous systems is proved, characterizing class of symmetries which bijection with quantities. Other classes preserve (up conformal factor) additional structures, such as form or function, also studied. Furthermore, making use geometric structures extended tangent bundle, time-dependent Lagrangian introduced. The results illustrated several examples. particular, two-body problem friction presented, could be interesting celestial mechanics.