2
$\begingroup$

If I have two vectors $a$ and $b$, whose components are time varying, for example $$a=[a_x(t), a_y(t), a_z(t)]$$ $$b=[b_x(t), b_y(t), b_z(t)]$$ The dot product of these 2 vectors can be expressed as $$a\cdot b=\Vert{a}\Vert\cdot\Vert{b}\Vert\cdot \cos\phi_{ab}$$ I want to compute in closed form the variation of $\phi_{ab}$ with respect to time, that is, $\dot\phi_{ab}$. Is it possible to symbolically compute this? Can I also obtain in closed form the derivative of $a\cdot b$ with respect to time? Which software would you recommend to do these kind of calculations: Matlab, Mathematica or Maple? Any examples? In fact, I have derived closed-form expressions tediously by hand for several expressions of the type I have given here. I wish to cross-verify whether my derivations are correct.

  • 1
    http://www.wolframalpha.com/input/?i=differentiate+arccos%28%28a%28t%29d%28t%29%2Bb%28t%29e%28t%29%2Bc%28t%29f%28t%29%29%2F%28sqrt%28a%28t%29%5E2%2Bb%28t%29%5E2%2Bc%28t%29%5E2%29sqrt%28d%28t%29%5E2%2Be%28t%29%5E2%2Bf%28t%29%5E2%29%29%292011-10-13
  • 0
    @Bill Cook: Thank you. I tried using what you ve sent me. The expressions seem to be complicated though. Well. fair enough. But i was wondering if i could retain **a** and **b** and its derivatives *a'* and *b'* (w.r.t time)as vectors itself in the final expression.2011-10-14

1 Answers 1