NON-EQUILIBRIUM STATIONARY MODES OF BOUNDARY FRICTION
A non-equilibrium thermodynamic model describing the behavior of an ultrathin lubricating material film confined between two atomically-smooth solid surfaces is proposed. As the order parameter the excess volume is chosen whose value increases with melting and subsequent fluidization of lubricant. It is shown that the external pressure, applied perpendicularly to the friction surfaces, influences crucially the lubricant behavior. The total system of kinetic equations is written down in which the relative shear velocity of rubbing surfaces, their temperature, and external normal pressure are the control parameters. Phase diagram with domains of different friction regimes is built.
We consider a family of 4-dimensional Hamiltonian time-periodic linear systems depending on three parameters, λ1, λ2 and e such that for e=0 the system becomes autonomous. Using normal form techniques we study stability and bifurcations for e>0 small enough. We pay special attention to the d'Alembert case. The results are applied to the study of the linear stability of homographic solutions of the planar three-body problem, for some homogeneous potential of degree −α, 0