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Originally Posted by GUILLE But is there any such thing as radian is to rotation, but something is to another transalation? Is there a something like that for reflection, or translation, or enlargement, etz??? |
In analytical mechanics, the concept of angles, length, position, time, etc. become classified as generalized coordinates. All these are used in a particular type of transformations. For the transformation of rotation, the proper generalized coordinate to use are angles. For the translation, the proper generalized coordinate to use are distance, length or positions within a frame of reference. For reflection, the generalized coordinates also take on negative values. For enlargment, the generalized coordinates are rational scalar factors of multiplication.
In Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and gij are the components of the metric tensor G,