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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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/136246 |
| Acceso en línea: | http://hdl.handle.net/10261/136246 |
| Access Level: | acceso abierto |
| Palabra clave: | Rodrigues vector Rigid body kinematics Rotations |
| Sumario: | 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. |
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