def applyLagrangeCoeffs(r, v, f, g, f_dot, g_dot):
    """
    Apply the Lagrange coefficients to r and v.

    Parameters
    ----------
    r : `~numpy.ndarray` (3)
        Position vector in au.
    v : `~numpy.ndarray` (3)
        Velocity vector in au per day.
    f : float
        Langrange f coefficient.
    g : float
        Langrange g coefficient.
    f_dot : float
        Time deriviative of the Langrange f coefficient.
    g_dot : float
        Time deriviative of the Langrange g coefficient.

    Returns
    -------
    r_new : `~numpy.ndarray` (3)
        New position vector in au propagated with the Lagrange coefficients.
    v_new : `~numpy.ndarray` (3)
        New velocity vector in au per day propagated with the Lagrange coefficients.
    """
    r_new = f * r + g * v
    v_new = f_dot * r + g_dot * v

    return r_new, v_new