Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of quaternions nor avoid errors accumulated in the sense of long term time. We present symplectic geometric algorithms to deal with the quaternion kinematical differ...

Let $C_n$, $Q_n$ and $D_n$ be the cyclic group, quaternion group dihedral of order $n$, respectively. Recently, structures unit groups finite algebras $2$-groups that contain a normal subgroup index $2$ have been studied. The $D_{2n}, n\geq 3$ generalized $Q_{4n}, 2$ also $2$. $FQ_{12}$, $FD_{12}$, $F(C_2 \times Q_{12})$ D_{12})$ over field $F$ are well known. In this article, we continue inves...

. In this paper, we propose the cyclic decomposition of factor group , and  is Z-valued class functions direct product  under operation addition, is subgroup generalized characters .Then   an abelian denoted by  where quaternion order  and cyclic  Also, find the  rational  valued  characters  table  of   when prime numbers is&nbsp...

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

Abstract In this paper, we set ? ? ( G stretchy="false">) \eta(G) to be the number of conjugacy classes maximal cyclic subgroups a finite group ????. We compute for all metacyclic ????-groups. show that if ???? is ????-group order <m:msup...