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Simplifying the angle between two vectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104122] Simplifying the angle between two vectors
  • From: Mali_42 <bloomdalium at gmail.com>
  • Date: Tue, 20 Oct 2009 04:51:31 -0400 (EDT)

epicikloida[a_, b_][
  t_] := {(a + b) Cos[t] - b Cos[(a + b) t/b], (a + b) Sin[t] -
   b Sin[(a + b) t/b], 2 Sqrt[a*b + b^2] Cos[a t/2 b]}

depi := D[epicikloida[a, b][t], t]

Arccos[({0, 0, 1}*depi)/(Norm[{0, 0, 1}]*Norm[depi])]

I don't know how to simplfy last line. It needs to be  constant(angle
between vector (0,0,1 ) and tangent to epicycloid).
Thanks


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