def mom_v1_bulk(f, v1, v2, v3, integral_measure): return(integral_over_v(f * v1, integral_measure))
def density(f, v1, v2, v3, integral_measure): return(integral_over_v(f, integral_measure))
def q_q3(f, v1, v2, v3, integral_measure): return(integral_over_v(f * v3 * (v1**2 + v2**2 + v3**2), integral_measure ) )
def energy(f, v1, v2, v3, integral_measure): return(integral_over_v(0.5 * f * (v1**2 + v2**2 + v3**2), integral_measure ) )
def energy_q3(f, v1, v2, v3, integral_measure): return(integral_over_v(0.5 * f * v3**2, integral_measure ) )
def mom_rdot_bulk(f, rdot, thetadot, phidot, integral_measure): return(integral_over_v(f * rdot, integral_measure))
def q_q3(f, rdot, thetadot, phidot, integral_measure): return(integral_over_v(f * phidot * (rdot**2 + thetadot**2 + phidot**2), integral_measure ) )
def density(f, rdot, thetadot, phidot, integral_measure): return(integral_over_v(f, integral_measure))
def energy_q3(f, rdot, thetadot, phidot, integral_measure): return(integral_over_v(0.5 * f * phidot**2, integral_measure ) )
def energy(f, rdot, thetadot, phidot, integral_measure): return(integral_over_v(0.5 * f * (rdot**2 + thetadot**2 + phidot**2), integral_measure ) )