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In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold. The various charts on SO(3) set up rival coordinate systems: in this case there cannot be said to be a preferred set of parameters describing a rotation. There are three degrees of freedom, so that the dimension of SO(3) is three. In numerous applications one or other coordinate system is used, and the question arises how to convert from a given system to another.

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  • Charts on SO(3) (en)
  • Cartas sobre SO(3) (es)
  • SO(3)上的卡 (zh)
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  • In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold. The various charts on SO(3) set up rival coordinate systems: in this case there cannot be said to be a preferred set of parameters describing a rotation. There are three degrees of freedom, so that the dimension of SO(3) is three. In numerous applications one or other coordinate system is used, and the question arises how to convert from a given system to another. (en)
  • En matemáticas, el grupo ortogonal en tres dimensiones, también conocido como grupo de rotación SO(3), es un ejemplo natural de un variedad. Las diversas cartas sobre SO(3) configuran sistemas de coordenadas rivales: en este caso, no se puede decir que exista un conjunto preferido de parámetros que describan cualquier rotación. El sistema dispone de tres grados de libertad, por lo que la dimensión de SO(3) es tres. En numerosas aplicaciones se usa uno u otro sistema de coordenadas, y surge la pregunta de cómo convertir las coordenadas de un sistema dado en las de otro. (es)
  • 在数学中,三维空间内的特殊正交群,也被称为旋转群的SO(3),是一个典型的流形。在不同的SO(3)上的卡中,建立的坐标系互不相同:从这个角度讲,不能说哪种参数很适合描述旋转。由于存在三个自由度,因此SO(3)的维数是3。在不同的应用中需要使用不同的坐标系,因此如何从一个坐标系转换到另一个坐标系是一个潜在的问题。 (zh)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Space_of_rotations.png
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