quaternions and spatial rotation造句

• For the kinematics of rotation in three dimensions, see quaternions and spatial rotation.
• Thus quaternions are a preferred method for representing spatial rotations  see quaternions and spatial rotation.
• It is, in fact, already the subject of the article quaternions and spatial rotation.
• :: Quaternions are used to represent rotations in 3D and 4D space-see Quaternions and spatial rotation.
• The map from unit quaternions to rotations of 3D space described in quaternions and spatial rotation is also a universal cover.
• By way of contrast he notes that Felix Klein appears not to look beyond the theory of Quaternions and spatial rotation.
• Hence a selective merge of say, just the definition, to Versor or Quaternions and spatial rotation is an obvious alternative to deletion.
• There's an article on quaternions and spatial rotation which may be helpful .-- talk ) 20 : 41, 6 March 2008 ( UTC)
• Very similar formulas can be found in the article on quaternions and spatial rotations, which covers this from a purely mathematical viewpoint but does not cover electromagnetism.
• There is a natural 2-to-1 homomorphism from the group of unit quaternions to the 3-dimensional rotation group described at quaternions and spatial rotations.
• The diagram D 2 is two isolated nodes, the same as A 1 & cup; A 1, and this coincidence corresponds to the covering map homomorphism from SU ( 2 ) & times; SU ( 2 ) to SO ( 4 ) given by quaternion multiplication; see quaternions and spatial rotation.
• The binary icosahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism \ operatorname { Spin } ( 3 ) \ cong \ operatorname { Sp } ( 1 ) where Sp ( 1 ) is the multiplicative group of unit quaternions . ( For a description of this homomorphism see the article on quaternions and spatial rotations .)
• The binary tetrahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism \ operatorname { Spin } ( 3 ) \ cong \ operatorname { Sp } ( 1 ) where Sp ( 1 ) is the multiplicative group of unit quaternions . ( For a description of this homomorphism see the article on quaternions and spatial rotations .)
• The binary octahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism \ operatorname { Spin } ( 3 ) \ cong \ operatorname { Sp } ( 1 ) where Sp ( 1 ) is the multiplicative group of unit quaternions . ( For a description of this homomorphism see the article on quaternions and spatial rotations .)
• As a subgroup of the spin group, the binary cyclic group can be described concretely as a discrete subgroup of the unit quaternions, under the isomorphism \ operatorname { Spin } ( 3 ) \ cong \ operatorname { Sp } ( 1 ) where Sp ( 1 ) is the multiplicative group of unit quaternions . ( For a description of this homomorphism see the article on quaternions and spatial rotations .)