Wolfram Cloud Document

In[]:=

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))

In[]:=

P1c=D[Inverse[P1a],t];TraditionalForm[Simplify[P1c]]

Out[]//TraditionalForm=

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