This paper deals with the induced instability due to parametric resonance of rectangular
plates traversed by inertial loads and lying on elastic foundations. The extended Hamilton's …

A method to analyze the stability of satellites flying in low Earth orbits is presented. Starting
from the classical rotational equations of motion, including gravity gradient, the influence of …

The problem of an elastic beam under the periodic loading of successive moving masses is
investigated as a pragmatic case for studying dynamic stability of linear time-varying …

We consider a discrete dynamical system with internal degrees of freedom (DOF). Due to the
symmetry between the internal DOFs, certain internal modes cannot be excited by external …

Many physical phenomena might be modeled with the well-known Mathieu equation.
Engineering applications, such as wind turbine blade dynamics, and helicopter rotor …

Parametric excitation is epitomized by the Mathieu equation, x''+(d+ e cos t) x= 0, which
involves the characteristic feature of 2: 1 resonance. This thesis investigates three …

This paper deals with a class of conservative nonlinear oscillators of the form ̈ x (t)+ f (x
(t))= 0, where f (x) is analytic. A transformation of time from t to a new time coordinate τ is …

This manuscript describes how solutions of the Navier-Stokes equations behave in the large
scales when forced in the small scales. It analyzes also the large scale behavior of magnetic …

We consider second order ordinary differential equations describing periodically forced
dynamical systems with one and a half degrees of freedom. First, we study Hill's equation …

In this paper, instability due to occurrence of parametric resonance in transverse vibration of
a rectangular plate on an elastic foundation under passage of continuous series of moving …