Mean motions in conditionally periodic separable systems

Optimal periodic motions of two-mass systems in resistive media

Progressive motions of two-mass systems in resistive media are analyzed. The motion control is implemented by means of periodic relative displacements of the masses. Different kinds of resistance forces acting upon the system are considered, including linear and nonlinear resistance depending on the velocity, as well as Coulomb’s dry friction forces. Constraints are imposed on the relative disp...

Quasi-periodic motions in strongly dissipative forced systems

We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing.

Expansions Forquasi Periodic Motions

Asymptotics of Damped Periodic Motions with Random

We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the distribution of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the rst time instant at which the velocity vanishes, a...

On bifurcations into nonresonant quasi-periodic motions

The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs mul...