3 ms·

I must be missing something major here, but given a sequence of rotations combined into a quaternion orientation, can’t you just get the inverse rotation back t

by ginko 1y ago

I must be missing something major here, but given a sequence of rotations combined into a quaternion orientation, can’t you just get the inverse rotation back to the original orientation by inverting the quaternion?

ogogmad 1y ago
I think even conjugating it. The formula for rotation via quats is v->qvq^{-1} = qvq^*/|q|^2.
cormacrelf 1y ago
You can absolutely do that and there is nothing for general linear algebra libraries to do. The actual paper is very clear about what it's for: https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf It says: Consider now a general time-dependent field B(t) of duration T. The pulse B(t) may be extremely convoluted ... Can one make the field B(t) return the system to its original state at the end of the pulse...? This pulse is modelled as a long sequence of rotations. For maths purposes if you had such a sequence, you can obviously just multiply all the rotations together and find the inverse very easily. For physics purposes, you don't really have access to each individual rotation, all you can do is tune the pulse. Creating an "inverse pulse" is quite unwieldy, you might literally need to create new hardware. The paper asks "what if we just amplified the pulse? Can we change this alone and make it not impart any rotation?" They are trying to take any pulse B(t) and zero out any rotation it imparts on some particle or whatever by uniformly tuning the field’s magnitude, B(t) → λB(t) or by uniformly stretching or compressing time, B(t) → B(λt) And the answer is that you can do that, but you might have to perform the pulse twice.
- oh_my_goodness 1y ago
  So it’s similar thinking to spin echoes. https://en.wikipedia.org/wiki/spin_echoes https://en.wikipedia.org/wiki/spin_echoes

3 ms·

I must be missing something major here, but given a sequence of rotations combined into a quaternion orientation, can’t you just get the inverse rotation back t

by ginko 1y ago

ogogmad 1y ago
I think even conjugating it. The formula for rotation via quats is v->qvq^{-1} = qvq^*/|q|^2.
cormacrelf 1y ago
You can absolutely do that and there is nothing for general linear algebra libraries to do. The actual paper is very clear about what it's for: https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf https://fiteoweb.unige.ch/~eckmannj/ps_files/ETPRL.pdf It says: Consider now a general time-dependent field B(t) of duration T. The pulse B(t) may be extremely convoluted ... Can one make the field B(t) return the system to its original state at the end of the pulse...? This pulse is modelled as a long sequence of rotations. For maths purposes if you had such a sequence, you can obviously just multiply all the rotations together and find the inverse very easily. For physics purposes, you don't really have access to each individual rotation, all you can do is tune the pulse. Creating an "inverse pulse" is quite unwieldy, you might literally need to create new hardware. The paper asks "what if we just amplified the pulse? Can we change this alone and make it not impart any rotation?" They are trying to take any pulse B(t) and zero out any rotation it imparts on some particle or whatever by uniformly tuning the field’s magnitude, B(t) → λB(t) or by uniformly stretching or compressing time, B(t) → B(λt) And the answer is that you can do that, but you might have to perform the pulse twice.
- oh_my_goodness 1y ago
  So it’s similar thinking to spin echoes. https://en.wikipedia.org/wiki/spin_echoes https://en.wikipedia.org/wiki/spin_echoes