相关论文: Quaternions in molecular modeling

This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…

The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…

Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…

In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…

The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…

This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…

Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…

This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the…

This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…

Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…

As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…

From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through…

Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…

We explain the use of dual quaternions to represent poses, twists, and wrenches.

An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…