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Has anyone here ever seen a good explanation of why quaternion multiplication maps to rotation concatenation?
by wtracy 13y ago
Has anyone here ever seen a good explanation of why quaternion multiplication maps to rotation concatenation?
- maxerickson 13y agoAs much as anything, it is a chosen property of the system. If you want to insist that mathematics is discovered (rather than invented), you can still say that this particular decomposition of vectors is prevalent because it has useful properties.
- ajkjk 13y agoI think of it as the opposite: there exists a Lie group of spatial rotations, so we want to use it, and we found a relatively convenient notation. There are many other kinds of 'complex' numbers (http://en.wikipedia.org/wiki/Hypercomplex_number http://en.wikipedia.org/wiki/Hypercomplex_number) - but you probably won't hear about them outside of mathematics and physics because they're less useful. The same applies to 2d - the SO(2) group exists; we map it to the complex numbers because it's convenient to do math with.
- T-A 13y agoHow about http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion_rotation_operations http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotatio...