Complicated Rotation

• To: mathgroup at smc.vnet.net
• Subject: [mg27237] Complicated Rotation
• From: Yas <yast at optushome.com.au>
• Date: Tue, 13 Feb 2001 03:35:44 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear mathgroup,
I have a problem that I have been trying to do in mathematica. I have a
number of functions defined as,

f1[t_]:=c Sin[t]
f2[t_]:=d Cos[t]
f3[t_]:=Sqrt[f1^2 + f2^2]
x[t_]:=ArcCos[f1/f2]
y[t_]:=g Sec[x]

where c, d and g are constants.

In addition I have a 3x3 matrix

with elements

{{a11,a12,a13},{a21,a22,a23},{a31,a32,a33}}

and each of the elements of the matrix can be defined as a function of t: ie.

a11[t_]:=Sin[b]^2 Cos[y] + Cos[x]^2   etc, etc,

where b can be constant.

I want to multiply the matrix by a unit initial vector s0 = {1,0,0}.

So I have defined the matrix as r[t_].

And the final vector

sf[t_] = r.s0.

So at t = 0, sf = s0.

And at successive increments of time

sf[1] = r[1]*s0
sf[2] = r[2]*sf[1]
sf[3] = r[3]*sf[2]
|
|
sf[n] = r[n]*sf[n-1]

Unfortunately I am not much of a programmer and I have had various attempts
with Map and Do and Table constructs with various errors. Could someone
please explain a method whereby I could get a list of sf values so that I
can plot sf versus time.