Brilliant! Thank you.
On Wednesday, February 15, 2017 at 3:35:24 PM UTC-6, Jason Moore wrote: > > 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 <spl...@gmail.com > <javascript:>> 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+un...@googlegroups.com <javascript:>. >> To post to this group, send email to sy...@googlegroups.com <javascript:> >> . >> 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/4e28b2c6-5d6f-49a3-b75e-19fa1424c924%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
