Visualizing rotations and composition of rotations with the Rodrigues vector

The purpose of this paper is to show that the mathematical treatment of three-dimensional rotations can be simplified, and its geometrical understanding improved, using the Rodrigues vector representation. We present a novel geometrical interpretation of the Rodrigues vector. Based on this interpret...

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Detalhes bibliográficos
Autor: González Valdenebro, Ángel
Formato: artículo
Fecha de publicación:2016
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/136246
Acesso em linha:http://hdl.handle.net/10261/136246
Access Level:acceso abierto
Palavra-chave:Rodrigues vector
Rigid body kinematics
Rotations
Descrição
Resumo:The purpose of this paper is to show that the mathematical treatment of three-dimensional rotations can be simplified, and its geometrical understanding improved, using the Rodrigues vector representation. We present a novel geometrical interpretation of the Rodrigues vector. Based on this interpretation and simple geometrical considerations, we derive the Euler–Rodrigues formula, Cayley's rotation formula and the composition law for finite rotations. The level of this discussion should be suitable for undergraduate physics or engineering courses where rotations are discussed.