We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with thedifference of temperatures between components even if bulkviscosities are null. The non-equilibrium dynamical pressure can bemeasured and may be convenient in several physical situations asfor example in cosmological circumstances where a dynamicalpressure played a major role in the evolution of the earlyuniverse.

In the tracking control of manipulators via the sliding scheme, it may happen that sometimes, because of various inaccuracies, the definition of the actual sliding surface involves errors terms which may be either deterministic or, on the contrary, stochastic. This paper considers this last case and shows how one can estimate the new performances of the system so disturbed. A stochastic Hamilton's principle is applied, by combining the Lagrange parameter technique with results of the dynamic programming approach.

It is shown that if one comes back to the formulation of the Hamilton's variational principle, it is then possible to obtain new viewpoints on the tracking control of robot manipulators. First, the Lagrange multiplier associated to the sliding surface can be interpretated in terms of control effort and/or forces of reaction of the mechanical system. Secondly, one can use the Taylor expansion of the mechanical Lagrangian, combined with a neighbour- ing Hamilton's principle, to obtain control schemes via sliding surfaces. Thirdly, a perturbation approach combined with the neighbouring Hamilton's principle provides results on the robustness of the control.