In this article, we give a general form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized (3PGQs) and study various properties applications. Firstly present definiton, multiplication table algebraic 3PGQs. matrix representation Hamilton operators for derive polar represenation, De Moivre’s Euler’s formulas with representations Additionally, relations betwee...

As mathematicians found out in the last century, there are only four normed division algebras1 over ℝ: real numbers themselves, complex numbers, quaternions and octonions. Whereas very well-known most of their properties carry to (apart from fact that these not commutative), octonions different harder handle since they even associative. However, can be used for several interesting topological c...

This paper proposes a nonlinear adaptive position and attitude tracking controller for satellite proximity operations between a target and a chaser satellite. The controller requires no information about the mass and inertia matrix of the chaser satellite, and takes into account the gravitational acceleration, the gravity-gradient torque, the perturbing acceleration due to Earth’s oblateness, a...