The Jacobi–Maupertuis metric allows one to reformulate Newton’s equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of the boundary contains pairs of conjugate points close to the boundary. We prove the conjugate locus of any point near enough to the boundary is a hypersurfa...

Air-film damping, which dominates over other losses, plays a significant role in the dynamic response of many micro-fabricated devices with a movable mass suspended by various bearing mechanisms. Modeling the damping characteristics accurately will be greatly helpful to the bearing design, control, and test in various micromotor devices. This paper presents the simulated and experimental squeez...

Abstract The identification of the modal parameters from frequency response functions is a subject that is not new. However, the starting point often comes from the equations that govern the dynamic motion. In this paper, a novel approach is shown, resulting from an analysis that starts on the dissipated energy per cycle of vibration. Numerical and experimental examples were used in order to as...

The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of interaction matrices leading to the concentration of waves in a chosen partial channel and spatial localization are shown. The limiting instructive cases ill...

A two-dimensional generalized hydrodynamics (GH) model is developed to study the full spectrum of both longitudinal and transverse dust acoustic waves (DAW) in strongly coupled complex (dusty) plasmas, with memory-function-formalism being implemented to enforce high-frequency sum rules. Results are compared with earlier theories (such as quasi-localized charge approximation and its extended ver...

The effect of an increase in speed relative to the speed of sound on the unsteady flow round a harmonically oscillating aerofoil, is to increase the lag of the aerodynamic forces and moments behind the deflection when the frequency is small. It is shown theoretically that this will result in a serious deterioration of the damping of both the lateral oscillation and the high frequency longitudin...