Wikipedia:Reference desk/Archives/Mathematics/2011 July 30

= July 30 =

mathematics
my hundreds digit is 3 more than my ones digit and my tens digit is 1 more than my hundreds digit what numbers can i be? — Preceding unsigned comment added by 112.206.73.68 (talk) 01:41, 30 July 2011 (UTC)
 * Sooner or later I will learn to stop looking at Wikipedia on Friday evening. Looie496 (talk) 01:59, 30 July 2011 (UTC)
 * That's less than a thousand cases to check by hand; no biggie. Get on it, anon! --COVIZAPIBETEFOKY (talk) 02:20, 30 July 2011 (UTC)
 * For future reference, please avoid giving questions such a nonspecific title as mathematics. Every question asked here is supposed to be about mathematics; your title should say what is different about your particular question. --Trovatore (talk) 03:00, 30 July 2011 (UTC)
 * The complete list of three digit numbers satisfying those conditions is 340, 451, 562, 673, 784, 895. Any number with more than three digits will be valid if the last three digits are any of those combinations too.Widener (talk) 03:51, 30 July 2011 (UTC)
 * I feel for you, I am not a number, I am a free man Dmcq (talk) 07:43, 30 July 2011 (UTC)

Quaternion/matrix differential equation
I am trying to solve $$ \frac{d}{dt} \log(A(t)B) = 0 $$ for $$B$$, where $$A(t)$$ and $$B$$ are quaternions. Does anyone know how I should approach this problem? I don't believe that I can assume commutativity of $$A(t)$$ and $$B$$, but in case I'm wrong, does anyone know a simple way of finding a solution if they do commute? I have code to test such a solution numerically, so any ideas are welcome.--Leon (talk) 09:31, 30 July 2011 (UTC)
 * It might be better if you could tell us why you need to solve this problem. What is the motivation? Why do you need to solve this problem? What progress have you made towards solving this problem? Remember that the reference desk is not a homework solution resource. If you have encountered this problem in your own work then you will be able to give us ample motivation. If it is a homework problem then you will be able to give us your current ideas and attempt. — Fly by Night  ( talk )  01:23, 31 July 2011 (UTC)
 * Okay, I'm trying to extend the notion of curvature for curves in $$\mathbb{R}^3$$ to the (double-cover of the) space of rotations, $$\text{Spin}^3$$, and was hoping to define a radius of curvature by the amount of rotation (angle) associated with a spherical-linear motion from some orientation $$B$$ to an orientation on the (arbitrary) rotational motion $$A(t)$$ ($$A(t)$$ is an orientation that varies smoothly with time and defines a rotational motion). To meaningfully define a radius of curvature, the angle of rotation associated with a motion from $$A(t)$$ (which is the rotational motion I'm ultimately interested in) to $$B$$ should be approximately a constant for a small variation in $$t$$.  Now if THAT sounds like homework then education must have changed a lot since I went to school!--Leon (talk) 11:32, 31 July 2011 (UTC)


 * This question looks nothing like homework, and even if it is, its phrasing is a far cry from the "solve my HW for me" crowd. Explaining the motivation for a question was never a requirement here. -- Meni Rosenfeld (talk) 08:22, 31 July 2011 (UTC)
 * I don't have much experience with quaternions, but wouldn't you be able to say that since $$ \frac{d}{dt} \log(A(t)B) = 0 $$, $$\log(A(t)B)$$ is constant and so $$A(t)B$$ is constant? So $$B=A(t)^{-1}c$$, and if B is supposed to be a constant then $$A(t)$$ must be constant? -- Meni Rosenfeld (talk) 08:22, 31 July 2011 (UTC)
 * That's what I figured shortly after writing the question. However, given the above, have you any ideas where I may be going wrong?--Leon (talk) 11:32, 31 July 2011 (UTC)