The SU(2) Spinor Map: Rotation Composition by Graphical Quaternion Triangles
The SU(2) Spinor Map: Rotation Composition by Graphical Quaternion Triangles
This Demonstration shows the spherical triangle congruences needed to understand the relationship between unit quaternion multiplication (i.e. the group ), spatial rotations in the adjoint representation , and a graphical quaternion multiplication construction conceived by William Rowan Hamilton [3]. Drag the triangle vertices using the 2D sliders. Use the "time" slider to see the congruences between the central triangle formed by vertices , , and the three triangles , , and . Use the "show congruence" checkbox to show or hide the moving triangles, "show labels" to show or hide labels, "show vertex vectors" to show the position vectors of the vertices , , , and "show inner triangle only" to show the quaternion arc composition triangle alone.
SU(2)
SO(3)
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b
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R
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R
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R
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