in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

in this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the hermitian matrix expression $$‎ ‎f(x,y)=c_{4}-b_{4}y-(b_{4}y)^{*}-a_{4}xa_{4}^{*},$$ where $c_{4}$ is‎ ‎hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$x$ and $y$ satisfy‎ ‎the following consistent system of matrix equations $a_{3}y=c_{3}‎, ‎a_{1}x=c_{1},xb_{1}=d_{1},a_{2}xa_{2}^{*}=c_{2},x=x^{*}.$ as‎ ‎consequences‎, ‎we g...

In this paper, an adaptive attitude control algorithm is developed based on neural network for a satellite using four reaction wheels in a tetrahedron configuration. Then, an attitude control based on feedback linearization control is designed and uncertainties in the moment of inertia matrix and disturbances torque have been considered. In order to eliminate the effect of these uncertainties, ...

Let p1, . . . , pn be positive real numbers. It is well known that for every r < 0 the matrix [(pi + pj) r ] is positive definite. Our main theorem gives a count of the number of positive and negative eigenvalues of this matrix when r > 0. Connections with some other matrices that arise in Loewner’s theory of operator monotone functions and in the theory of spline interpolation are discussed.

in this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step timoshenko rotor carrying concentrated masses is presented. each attached element is considered to have both translational and rotational inertia. forward and backward frequencies and corresponding modes are obtained using transfer matrix method (tmm). the effect of the angular velocity of spin,...

in this paper, an adaptive attitude control algorithm is developed based on neural network for a satellite using four reaction wheels in a tetrahedron configuration. then, an attitude control based on feedback linearization control has been designed and uncertainties in the moment of inertia matrix and disturbances torque have been considered. in order to eliminate the effect of these uncertain...

the well-known electro-mechanical analogy that equates current, voltage, resistance, inductance and capacitance to force, velocity, damping, spring constant and mass has a shortcoming in that mass can only be used to simulate a capacitor which has one terminal connected to ground. a new model that was previously proposed by the authors that combines a mass with a pulley (mp) is shown to simulat...

This paper explores how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. It demonstrates that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike what happens for nonzero patterns. A class of patterns is developed that are refined inertially arbitrary but not spectrally arbitrary, making use o...

In this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step Timoshenko rotor carrying concentrated masses is presented. Each attached element is considered to have both translational and rotational inertia. Forward and backward frequencies and corresponding modes are obtained using transfer matrix method (TMM). The effect of the angular velocity of spin,...