Tensor of a quaternion: Difference between revisions

Revision as of 19:58, 27 March 2009

Revision as of 20:11, 27 March 2009

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Here t and t' are reals.

=Properties of Tensors=

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The tensor of a unit vector is equal to one, if <math>\alpha</math>

Hamilton proved that the tensor of a quaternion is equal to the square root of the [[Classical_Hamiltonian_quaternions#Common_norm|common norm]].

In symbols this can be written:

<math>\mathbf{T}q = \sqrt{\mathbf{N}q}=\sqrt{q\mathbf{k}q}</math>

Hamilton also proved that if q is written as

<math>q = w + xi + yj + zk\,</math>

then

<math>\mathbf{T}q = \sqrt{w^2 + x^2 + y^2 = z^2}</math>

=Applications=

==Stresses and Strains==