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...

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...

Finding the mean (average) of n arbitrary 3D rotations or orientations is conceptually challenging both in its algebra and its geometric interpretation. To my knowledge, no solutions have been found for the general case, although a number of approximate solutions have been proposed [3, 4, 5] to accurately and e ciently handle those limiting cases typical of engineering interest. This report pro...