A simple and easy-to-implement method that guarantees the effective active synchronization of a chaotic gyroscopic system within a specified settling time limit is presented. A closed-form expression is given for the determination of the appropriate synchronizing control signal. The method is successfully validated through simulations for various initial conditions of the gyroscopic system.

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hex...

Gyroscopic alignment of a fluid occurs when flow structures align with the rotation axis. This often gives rise to highly spatially anisotropic columnar that in combination complex domain boundaries pose challenges for efficient numerical discretizations and computations. We define gyroscopic polynomials be three-dimensional expressed coordinate system conforms rotational alignment. remap origi...

This paper extends the λ-method, which was developed in (Auckly et al., 2000; Auckly and Kapitanski, 2003) to solve effectively PDE’s involved in the method of controlled Lagrangian systems, by taking into account a gyroscopic term. The gyroscopic force provides more free parameters when one designs stabilizing controllers in the method of controlled Lagrangian systems. We illustrate the extend...

in this paper, a theorem is derived for the existence of a common quadratic Lyapunov function for stability analysis of linear gyroscopic dynamic systems. A new method based on stochastic stability. In this paper we study the stochastic stability properties of linear gyroscopic dynamic systems.

Keywords: Second order differential systems Saddle point theorem Generalized Ahmad–Lazer–Paul type condition a b s t r a c t Existence of periodic solutions to second order differential systems with gyroscopic forces is considered via variational methods, where a generalized Ahmad–Lazer–Paul type condition is used. We do not impose the condition that the gyroscopic forces are small.

This paper investigates the bending vibration of rotating single-walled carbon nanotubes (SWCNTs) based on nonlocal theory. To this end, the rotating SWCNTs system modeled as a beam with a circular cross section and the Euler-Bernoulli beam theory (EBT) is applied with added effects such as rotary inertia, gyroscopic effect and rotor mass unbalance. Using nonlocal theory, two coupled sixth orde...