Code:

import pybullet as pbimport numpy as npimport timeimport pybullet_dataimport pdbphysicsClient = pb.connect(pb.GUI)#or pb.DIRECT for non-graphical versionpb.setAdditionalSearchPath(pybullet_data.getDataPath()) #optionallypb.setGravity(0,0,0)planeId = pb.loadURDF("plane.urdf")r2d2StartPos = [0,0,1] # elevated# originally facing green. So Z with no rotation points along green (Y)# points R2 diagonally (via yaw rotation around Z)r2d2StartOrientation = pb.getQuaternionFromEuler([0,0,0.785398163397448])# load the robotr2d2Id = pb.loadURDF("r2d2.urdf",r2d2StartPos, r2d2StartOrientation)# set rotational velocity same direction as robot is facing.pb.resetBaseVelocity(1,(0,0,0),(-1, -1,0))# goal is to see rot velocity relative to R2's orientation# so X should be non-zero, and Y,Z both at zero.for i in range (10000):pb.stepSimulation()time.sleep(1./240.)r2d2Vel = pb.getBaseVelocity(r2d2Id)r2d2Pos, r2d2Orn = pb.getBasePositionAndOrientation(r2d2Id)r2d2ornEuler = pb.getEulerFromQuaternion(r2d2Orn)yaw = r2d2ornEuler[2]# I noticed this first in the link mentioned in my first post.# this is a "basic rotation around Z# see https://en.wikipedia.org/wiki/Rotation_matrix "Basic Rotations"rot_around_z = np.array([[np.cos(-yaw), -np.sin(-yaw), 0],[np.sin(-yaw), np.cos(-yaw), 0],[0, 0, 1]])# once we have that, we want to see what the world-frame rotations# are translated via rot_around_zwx, wy, wz = np.dot(rot_around_z, r2d2Vel[1])print(wx, wy, wz)pb.disconnect()