  Turnpikes have recently gained significant research interest in optimal
control, since they allow for pivotal insights into the structure of solutions
to optimal control problems. So far, mainly steady state solutions which serve
as optimal operation points, are studied. This is in contrast to time-varying
turnpikes, which are in the focus of this paper. More concretely, we analyze
symmetry-induced velocity turnpikes, i.e. controlled relative equilibria,
called trim primitives, which are optimal operation points regarding the given
cost criterion. We characterize velocity turnpikes by means of dissipativity
inequalities. Moreover, we study the equivalence between optimal control
problems and steady-state problems via the corresponding necessary optimality
conditions. An academic example is given for illustration.

Systems and Control;Systems and Control;Optimization and Control