Darboux Vector
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry, especially the theory of space curves, the Darboux vector is the areal velocity vector of the Frenet frame of a space curve. It is named after Gaston Darboux who discovered it. It is also called angular momentum vector, because it is directly proportional to angular momentum.Let a rigid object move along a regular curve described parametrically by (t). This object has its own intrinsic coordinate system. As the object moves along the curve, l...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry, especially the theory of space curves, the Darboux vector is the areal velocity vector of the Frenet frame of a space curve. It is named after Gaston Darboux who discovered it. It is also called angular momentum vector, because it is directly proportional to angular momentum.Let a rigid object move along a regular curve described parametrically by (t). This object has its own intrinsic coordinate system. As the object moves along the curve, let its intrinsic coordinate system keep itself aligned with the curve''s Frenet frame. As it does so, the object''s motion will be described by two vectors: a translation vector, and a rotation vector , which is an areal velocity vector: the Darboux vector.
