This paper describes a procedure for incorporating artificial gyroscopic forces in the method of controlled Lagrangians. These energy-conserving forces provide additional freedom to expand the basin of stability and tune closed-loop system performance. We also study the effect of physical dissipation on the closed-loop dynamics and discuss conditions for stability in the presence of natural dam...

In this paper, the efficiency of the gyroscopic mounting method is studied for a highly dynamic GNSS receiver's reference oscillator for reducing signal loss. Analyses are performed separately in two phases, atmospheric and upper atmospheric flights. Results show that the proposed mounting reduces signal loss, especially in parts of the trajectory where its probability is the highest. This redu...

We present two methods for calculating resonant frequencies and mode shapes for fluid-structure vibration problems. We model the fluid-structure interaction problem using the #-V-P, finite element technique. This eigenproblem is more complicated than for ordinary structural analyses, as the formulation produces a quadratic eigenproblem (similar to those for gyroscopic systems). We derive proper...

We consider the numerical solution of quadratic eigenproblems with spectra that exhibit Hamiltonian symmetry. We propose to solve such problems by applying a Krylov-Schur-type method based on the symplectic Lanczos process to a structured linearization of the quadratic matrix polynomial. In order to compute interior eigenvalues, we discuss several shift-and-invert operators with Hamiltonian str...

We consider a gyroscopic system with two degrees of freedom under the action of small dissipative and non-conservative positional forces, which has its origin in the models of rotating bodies of revolution being in frictional contact. The spectrum of the unperturbed gyroscopic system forms a ”spectral mesh” in the plane ”frequency – gyroscopic parameter” with double semi-simple purely imaginary...

1 Mathematics Department, Preparatory Year Deanship, UmmAl-Qura University, P.O. Box 5555, Makkah 21955, Saudi Arabia 2 Faculty of Science, Tanta University, P.O. Box 31527, Tanta, Egypt 3 Mathematics Department, Faculty of Girls Education and Science, Taif University, Al-Khurmah Branch, P.O. Box 888, Taif 21974, Saudi Arabia 4 Electricity Department, Faculty of Engineering, Umm Al-Qura Univers...

Described in this paper is a Self-Stabilizing Hybrid Bicycle. Gyroscope technology implemented to develop the balancing forces achieve stability on all terrains. The main principle revolves around generating counteracting torque help stabilize tilting action of vehicle. Along with this, we have introduced hybrid system prime cycle when rider tired. includes battery which can be charged by three...