def earth_rates(ATTITUDE):
    """return angular velocities in earth frame"""
    from math import sin, cos, tan, fabs
    p = ATTITUDE.rollspeed
    q = ATTITUDE.pitchspeed
    r = ATTITUDE.yawspeed
    phi = ATTITUDE.roll
    theta = ATTITUDE.pitch
    psi = ATTITUDE.yaw
    phiDot = p + tan(theta) * (q * sin(phi) + r * cos(phi))
    thetaDot = q * cos(phi) - r * sin(phi)
    if fabs(cos(theta)) < 1e-20:
        theta += 1e-10
    psiDot = (q * sin(phi) + r * cos(phi)) / cos(theta)
    return phiDot, thetaDot, psiDot
