A model for synchronization of globally coupled phase oscillators including "inertial" effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized) and synchronized states of the oscillator population. Assuming a Lorentzian distribution of oscillator natural frequencies, g(Omega), both larger inertia or lar...

Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function W = W (ρ, ρ̇), is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small volume concentration of gas bubbles, and the dispersive shallow water model. These models are obt...

the optimum shape of balance weights is determined, using two different criteria. according to one, one of the balance weights should have minimum size. while the other requires that the mass moment of inertia about the axis of rotation should be minimum. in the second case, the calculus of variation is used to determine the optimum shape. graphs are presented to enable designers to find the di...

By making use of the notions and the notations from [12], we present the bounded delays, the absolute inertia and the relative inertia.