In this paper, we explain how dual quaternion theory can extend to quaternions with generalized complex number (GCN) components. More specifically, algebraically examine new type and give several matrix representations both as a GCN.

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary sufficient solvability conditions for a system Sylvester-type quaternion matrix equations, give an expression general solution to when it is solvable. As application system, consider special symmetry solution, named η-Hermitian equations. Moreover, present algorithm numerical example verif...

In this article we thoroughly investigate the possibility of employing the exact computation of the free rigid body motion as a component of splitting methods for problems of rigid bodies subject to external forces. We review various matrix and quaternion representations of the solution of the free rigid body equation, which involve Jacobi ellipic functions and elliptic integrals, and are amena...

The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control ISMC is applied to combine the first-order sliding modewith optimal control and is used to control quaternion-based spacecraft attitudemanoeuvres with externa...

In this paper, an approach is proposed to improve the numerical precision at the sound field simulation by the finite-difference time-domain (FDTD) method. The FDTD method is a numerical solution for the wave equation, proposed by R. Courant. Although it has achieved to simulate wave propagation by numerical solution for the wave equation, it causes numerical dispersions due to their approximat...

Claims were made in an article by Wang and Ma in 2013 that they had devised an algorithm for the quaternion LU decomposition that was significantly faster than the LU decomposition implemented in the Quaternion Toolbox for Matlab (QTFM). These claims have been tested and found to be unsupported by Matlab code supplied to the author by Wang and Ma. The author’s tests are presented, and test code...