How to use the poliastro.core.util.norm function in poliastro

Six component state vector [x, y, z, vx, vy, vz] (km, km/s).
    k : float
        gravitational constant, (km^3/s^2)
    J2: float
        oblateness factor
    R: float
        attractor radius

    Note
    ----
    The J2 accounts for the oblateness of the attractor. The formula is given in
    Howard Curtis, (12.30)

    """
    r_vec = state[:3]
    r = norm(r_vec)

    factor = (3.0 / 2.0) * k * J2 * (R ** 2) / (r ** 5)

    a_x = 5.0 * r_vec[2] ** 2 / r ** 2 - 1
    a_y = 5.0 * r_vec[2] ** 2 / r ** 2 - 1
    a_z = 5.0 * r_vec[2] ** 2 / r ** 2 - 3
    return np.array([a_x, a_y, a_z]) * r_vec * factor

def a_d(t0, u_, k):
        r = u_[:3]
        v = u_[3:]
        nu = rv2coe(k, r, v)[-1]
        beta_ = beta_0_ * np.sign(
            np.cos(nu)
        )  # The sign of ß reverses at minor axis crossings

        w_ = cross(r, v) / norm(cross(r, v))
        accel_v = f * (np.cos(beta_) * thrust_unit + np.sin(beta_) * w_)
        return accel_v

H0 : float
        atmospheric scale height, (km)
    rho0: float
        the exponent density pre-factor, (kg / m^3)

    Note
    ----
    This function provides the acceleration due to atmospheric drag. We follow
    Howard Curtis, section 12.4
    the atmospheric density model is rho(H) = rho0 x exp(-H / H0)

    """
    H = norm(state[:3])

    v_vec = state[3:]
    v = norm(v_vec)
    B = C_D * A / m
    rho = rho0 * np.exp(-(H - R) / H0)

    return -(1.0 / 2.0) * rho * B * v * v_vec

mass of the spacecraft (kg)
    Wdivc_s : float
        total star emitted power divided by the speed of light (W * s / km)
    star: a callable object returning the position of star in attractor frame
        star position

    Note
    ----
    This function provides the acceleration due to star light pressure. We follow
    Howard Curtis, section 12.9

    """

    r_star = star(t0)
    r_sat = state[:3]
    P_s = Wdivc_s / (norm(r_star) ** 2)

    nu = float(shadow_function(r_sat, r_star, R))
    return -nu * P_s * (C_R * A / m) * r_star / norm(r_star)

star: a callable object returning the position of star in attractor frame
        star position

    Note
    ----
    This function provides the acceleration due to star light pressure. We follow
    Howard Curtis, section 12.9

    """

    r_star = star(t0)
    r_sat = state[:3]
    P_s = Wdivc_s / (norm(r_star) ** 2)

    nu = float(shadow_function(r_sat, r_star, R))
    return -nu * P_s * (C_R * A / m) * r_star / norm(r_star)

ecc_f : float
        Final eccentricity.
    inc_f : float
        Final inclination.
    f : float
        Magnitude of constant acceleration.
    """

    # We fix the inertial direction at the beginning
    ecc_0 = ss_0.ecc.value
    if ecc_0 > 0.001:  # Arbitrary tolerance
        ref_vec = ss_0.e_vec / ecc_0
    else:
        ref_vec = ss_0.r / norm(ss_0.r)

    h_unit = ss_0.h_vec / norm(ss_0.h_vec)
    thrust_unit = cross(h_unit, ref_vec) * np.sign(ecc_f - ecc_0)

    inc_0 = ss_0.inc.to(u.rad).value
    argp = ss_0.argp.to(u.rad).value

    beta_0_ = beta(ecc_0, ecc_f, inc_0, inc_f, argp)

    def a_d(t0, u_, k):
        r = u_[:3]
        v = u_[3:]
        nu = rv2coe(k, r, v)[-1]
        beta_ = beta_0_ * np.sign(
            np.cos(nu)
        )  # The sign of ß reverses at minor axis crossings

        w_ = cross(r, v) / norm(cross(r, v))

def a_d(t0, u_, k):
        r = u_[:3]
        v = u_[3:]
        nu = rv2coe(k, r, v)[-1]

        alpha_ = nu - np.pi / 2

        r_ = r / norm(r)
        w_ = cross(r, v) / norm(cross(r, v))
        s_ = cross(w_, r_)
        accel_v = f * (np.cos(alpha_) * s_ + np.sin(alpha_) * r_)
        return accel_v

Six component state vector [x, y, z, vx, vy, vz] (km, km/s).
    k : float
        gravitational constant, (km^3/s^2)
    third_body: a callable object returning the position of 3rd body
        third body that causes the perturbation

    Note
    ----
    This formula is taken from Howard Curtis, section 12.10. As an example, a third body could be
    the gravity from the Moon acting on a small satellite.

    """

    body_r = third_body(t0)
    delta_r = body_r - state[:3]
    return k_third * delta_r / norm(delta_r) ** 3 - k_third * body_r / norm(body_r) ** 3

frontal area of the spacecraft (km^2)
    m: float
        mass of the spacecraft (kg)
    H0 : float
        atmospheric scale height, (km)
    rho0: float
        the exponent density pre-factor, (kg / m^3)

    Note
    ----
    This function provides the acceleration due to atmospheric drag. We follow
    Howard Curtis, section 12.4
    the atmospheric density model is rho(H) = rho0 x exp(-H / H0)

    """
    H = norm(state[:3])

    v_vec = state[3:]
    v = norm(v_vec)
    B = C_D * A / m
    rho = rho0 * np.exp(-(H - R) / H0)

    return -(1.0 / 2.0) * rho * B * v * v_vec

k : float
        gravitational constant, (km^3/s^2)
    J3: float
        oblateness factor
    R: float
        attractor radius

    Note
    ----
    The J3 accounts for the oblateness of the attractor. The formula is given in
    Howard Curtis, problem 12.8
    This perturbation has not been fully validated, see https://github.com/poliastro/poliastro/pull/398

    """
    r_vec = state[:3]
    r = norm(r_vec)

    factor = (1.0 / 2.0) * k * J3 * (R ** 3) / (r ** 5)
    cos_phi = r_vec[2] / r

    a_x = 5.0 * r_vec[0] / r * (7.0 * cos_phi ** 3 - 3.0 * cos_phi)
    a_y = 5.0 * r_vec[1] / r * (7.0 * cos_phi ** 3 - 3.0 * cos_phi)
    a_z = 3.0 * (35.0 / 3.0 * cos_phi ** 4 - 10.0 * cos_phi ** 2 + 1)
    return np.array([a_x, a_y, a_z]) * factor