QUATÉRNIONS E AS ROTAÇÕES NO ESPAÇO

Abstract

The Quaternions were created in 1843 by W. R. Hamilton and its use, although not much publicized, it is not new. Basically, quaternions can be seen as an algebraic extension of complex numbers, in which it has three imaginary components instead of one, may be represented by 𝑎̇ = 𝑎 + 𝑎𝑥𝑖⃗ + 𝑎𝑦𝑗⃗ + 𝑎𝑧𝑘⃗⃗ = (𝑎, 𝑎⃗), where a is a scalar and (𝑎𝑥, 𝑎𝑦, 𝑎𝑧) are the vector components 𝑎⃗. Once specified some properties and basic operations, from this definition, we can prove that this initial concept, allowing the correlation between the algebra of quaternions. In this context, the aim of this paper is to present some basic concepts related to the Algebra of Quaternions, pointing out some aspects of this representation.

Keywords

• Quaternions
• Noncommutative Rings
• Complex Numbers
• W. R. Hamilton