If you take the Jacobian with respect to your b vector I think you should get A.
Jason moorepants.info +01 530-601-9791 On Wed, Feb 15, 2017 at 1:17 PM, Sebastian Luque <splu...@gmail.com> wrote: > Hello, > > I'm trying to work out the derivation of the relationship between Euler > angle rates in terms of Euler angles and angular rates in body frame > (e.g. http://dma.ing.uniroma1.it/users/lss_da/MATERIALE/Textbook.pdf > section 1.2.2). I have developed this for the so-called "Tait-Bryant" > rotation as follows: > > ---<--------------------cut here---------------start------ > ------------->--- > import sympy as sy > > def x_rotation(theta): > return sy.Matrix([[1, 0, 0], > [0, sy.cos(theta), -sy.sin(theta)], > [0, sy.sin(theta), sy.cos(theta)]]) > > def y_rotation(theta): > return sy.Matrix([[sy.cos(theta), 0, sy.sin(theta)], > [0, 1, 0], > [-sy.sin(theta), 0, sy.cos(theta)]]) > > def z_rotation(theta): > return sy.Matrix([[sy.cos(theta), -sy.sin(theta), 0], > [sy.sin(theta), sy.cos(theta), 0], > [0, 0, 1]]) > > phi, theta, psi = sy.symbols("\\phi, \\theta, \\psi") > > omega_x, omega_y, omega_z = sy.symbols("\\omega_x \\omega_y \\omega_z") > p, q, r = sy.symbols("p q r") > phi_dot, theta_dot, psi_dot = sy.symbols(("\\dot\\phi \\dot\\theta " > "\\dot\psi")) > omega_e = sy.Matrix([[omega_x], [omega_y], [omega_z]]) > omega_b = sy.Matrix([[p], [q], [r]]) > psi_b = ((x_rotation(phi).T * y_rotation(theta).T) * > sy.Matrix([[0], [0], [psi_dot]])) > theta_b = x_rotation(phi).T * sy.Matrix([[0], [theta_dot], [0]]) > phi_b = sy.Matrix([[phi_dot], [0], [0]]) > pqr = phi_b + theta_b + psi_b > ---<--------------------cut here---------------end-------- > ------------->--- > > The resulting `pqr' matrix is as expected: > > Out[57]: > > Matrix([ > [ \dot\phi - \dot\psi*sin(\theta)], > [\dot\psi*sin(\phi)*cos(\theta) + \dot\theta*cos(\phi)], > [\dot\psi*cos(\phi)*cos(\theta) - \dot\theta*sin(\phi)]]) > > However, this needs to be broken down into an expression of the form: > > A b > > where A is the 3x3 transformation matrix, and b is the vector with > \dot\phi, \dot\theta, and \dot\psi. I know what the result should be, > but don't know how to get sympy to do it. Any suggestions welcome. > > -- > Seb > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit https://groups.google.com/d/ > msgid/sympy/201748a8-3446-45c4-9779-d195c35cafcb%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/201748a8-3446-45c4-9779-d195c35cafcb%40googlegroups.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAP7f1Aj0fCJ1D-hB8pkh_Jm64vBU_hRhE%2Bz%3DxdYya8ZeJyPASA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
