Wolfram Cloud Document

R

1

={{1,0,0},{0,Cos[

θ

1

[t]],Sin[

θ

1

[t]]},{0,-Sin[

θ

1

[t]],Cos[

θ

1

[t]]}};

R

2

={{Cos[

θ

2

[t]],0,-Sin[

θ

2

[t]]},{0,1,0},{Sin[

θ

2

[t]],0,Cos[

θ

2

[t]]}};

R

3

={{Cos[

θ

3

[t]],Sin[

θ

3

[t]],0},{-Sin[

θ

3

[t]],Cos[

θ

3

[t]],0},{0,0,1}};

In[]:=

P1a=

R

3

.

R

2

.

R

1

;TraditionalForm[Simplify[P1a]]

Out[]//TraditionalForm=

cos( θ 2 (t))cos( θ 3 (t))	sin( θ 1 (t))sin( θ 2 (t))cos( θ 3 (t))+sin( θ 3 (t))cos( θ 1 (t))	sin( θ 1 (t))sin( θ 3 (t))-sin( θ 2 (t))cos( θ 1 (t))cos( θ 3 (t))
sin( θ 3 (t))(-cos( θ 2 (t)))	cos( θ 1 (t))cos( θ 3 (t))-sin( θ 1 (t))sin( θ 2 (t))sin( θ 3 (t))	sin( θ 1 (t))cos( θ 3 (t))+sin( θ 2 (t))sin( θ 3 (t))cos( θ 1 (t))
sin( θ 2 (t))	sin( θ 1 (t))(-cos( θ 2 (t)))	cos( θ 1 (t))cos( θ 2 (t))

Ideallythesetermswouldlooklike:

cosθ

1

sinθ

2

+

cosθ

2

sinθ

1

etc.