Notes on a barge model

barge.py

####Frames
Seabottom = SM.ReferenceFrame('Seabottom')
Barge_Frame = Seabottom.orientnew('Barge_Frame', 'Body', [phi_barge, theta_barge, psi_barge], 'XYZ')  #roll, pitch, yaw: phi, theta, psi
"""So in the line above you set the body fixed xyz angles (these
are Euler angles) of the barge, but in the line below you set the angular
velocity vector as Space fixed rotations. Before you set the angular velocity with explicit generalized speeds you should run this:

In [2]: Barge_Frame.ang_vel_in(Seabottom)
Out[2]: (sin(psi_barge)*theta_barge' + cos(psi_barge)*cos(theta_barge)*phi_barge')*Barge_Frame.x + (-sin(psi_barge)*cos(theta_barge)*phi_barge' + cos(psi_barge)*theta_barge')*Barge_Frame.y + (sin(theta_barge)*phi_barge' + psi_barge')*Barge_Frame.z

If your kinematical differential equations are going to be defined as:

omeagaphi_barge = phi_barge.dt()

Then you can see how the above does not match below.

One option would be to set your kinematical difff equations as:

[gen_speed_1 - (sin(psi_barge)*theta_barge' + cos(psi_barge)*cos(theta_barge)*phi_barge'),
 gen_speed_2 - (-sin(psi_barge)*cos(theta_barge)*phi_barge' + cos(psi_barge)*theta_barge'),
 gen_speed_2 - (sin(theta_barge)*phi_barge' + psi_barge')]

Barge_Frame.set_ang_vel(Seabottom, gen_speed_1*Barge_Frame.x + gen_speed_2*Barge_Frame.y + gen_speed_2*Barge_Frame.z)

But if you want

omeagaphi_barge = phi_barge.dt(), etc then you need to make sure things are consistent:

Barge_Frame.set_ang_vel(Seabottom, (sin(psi_barge)*omeagetheta_barge + cos(psi_barge)*cos(theta_barge)*omegaphi_barge)*Barge_Frame.x + (-sin(psi_barge)*cos(theta_barge)*omegaphi_barge + cos(psi_barge)*omegatheta_barge)*Barge_Frame.y + (sin(theta_barge)*omegaphi_barge + omegapsi_barge)*Barge_Frame.z)


"""
Barge_Frame.set_ang_vel(Seabottom, omegaphi_barge * Seabottom.x + omegatheta_barge * Seabottom.y + omegapsi_barge * Seabottom.z)