# Revision history [back]

### solving matrix equation

Could anyone tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But the matrix O equates to P. (I'm deriving what textbook didn't and just said that they are same.)

var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined.

theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t);

R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]])

R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]])

R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])

P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]])

R=R3R2R1

R_T=R.T; R_dev=R.derivative(t)

O=R_dev*R_T

view(O)

assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t?

### solving matrix equation

Could anyone please tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But I know that the matrix O equates equals to P. (I'm deriving what textbook didn't and just the textbook said that they are same.)

var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined.

theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t);

R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]])

R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]])

R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])

P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]])

R=R3R2R1

R_T=R.T; R_dev=R.derivative(t)

O=R_dev*R_T

view(O)

assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t?

### solving matrix equation

Could anyone please tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But I know that the matrix O equals to P. (I'm deriving what textbook didn't and the textbook said that they are same.)

var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined.

theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t);

R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]])

R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]])

R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])

P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]])

R=R3R2R1

R_T=R.T; R_dev=R.derivative(t)

O=R_dev*R_T

view(O)

assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t?

### solving matrix equation

Could anyone please tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But I know that the matrix O equals to P. (I'm deriving what textbook didn't and the textbook said that they are same.)

 var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined.

 theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t); R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]]) R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]]) R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]]) P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]]) R=R3'R=R3R2R1R1' R_T=R.T; R_dev=R.derivative(t) O=R_dev*R_T view(O) assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t? 5 No.5 Revision

### solving matrix equation

Could anyone please tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But I know that the matrix O equals to P. (I'm deriving what textbook didn't and the textbook said that they are same.)

 var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined.  theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t);psi=function('psi')(t);
R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]])1]])
R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]])cos(theta)]])
R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])
R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]]) P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]])0]])
'R=R3*R2*R1'
'R=R3R2R1'R_T=R.T; R_dev=R.derivative(t)
O=R_dev*R_T
R_T=R.T; R_dev=R.derivative(t) O=R_dev*R_T view(O)view(O)


assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t?

### solving matrix equation

Could anyone please tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But I know that the matrix O equals to P. (I'm deriving what textbook didn't and the textbook said that they are same.)

var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined.

theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t);

R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]])

R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]])

R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])

P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]])

'R=R3*R2*R1'
R=R3*R2*R1

R_T=R.T; R_dev=R.derivative(t)

O=R_dev*R_T

view(O)


assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t?