def pqw2ijk(pqw, inc, raan, argp):
"""Converts from perifocal to IJK.
"""
ijk = transform(pqw, -argp, 2)
ijk = transform(ijk, -inc, 0)
ijk = transform(ijk, -raan, 2)
return ijk
def coe2rv(k, p, ecc, inc, raan, argp, nu):
"""Converts from classical orbital elements to vectors.
Parameters
----------
k : float
Standard gravitational parameter (km^3 / s^2).
p : float
Semi-latus rectum or parameter (km).
ecc : float
Eccentricity.
inc : float
Inclination (rad).
omega : float
Longitude of ascending node (rad).
argp : float
Argument of perigee (rad).
nu : float
True anomaly (rad).
"""
r_pqw, v_pqw = rv_pqw(k, p, ecc, nu)
r_ijk = transform(r_pqw, -argp, 2)
r_ijk = transform(r_ijk, -inc, 0)
r_ijk = transform(r_ijk, -raan, 2)
v_ijk = transform(v_pqw, -argp, 2)
v_ijk = transform(v_ijk, -inc, 0)
v_ijk = transform(v_ijk, -raan, 2)
return r_ijk, v_ijk
def coe2rv(k, p, ecc, inc, raan, argp, nu):
"""Converts from classical orbital elements to vectors.
Parameters
----------
k : float
Standard gravitational parameter (km^3 / s^2).
p : float
Semi-latus rectum or parameter (km).
ecc : float
Eccentricity.
inc : float
Inclination (rad).
omega : float
Longitude of ascending node (rad).
argp : float
Argument of perigee (rad).
nu : float
True anomaly (rad).
"""
r_pqw, v_pqw = rv_pqw(k, p, ecc, nu)
r_ijk = transform(r_pqw, -argp, 2)
r_ijk = transform(r_ijk, -inc, 0)
r_ijk = transform(r_ijk, -raan, 2)
v_ijk = transform(v_pqw, -argp, 2)
v_ijk = transform(v_ijk, -inc, 0)
v_ijk = transform(v_ijk, -raan, 2)
return r_ijk, v_ijk
def coe2rv(k, p, ecc, inc, raan, argp, nu):
r"""Converts from classical orbital to state vectors.
Classical orbital elements are converted into position and velocity
vectors by `rv_pqw` algorithm. A rotation matrix is applied to position
and velocity vectors to get them expressed in terms of an IJK basis.
.. math::
\begin{align}
\vec{r}_{IJK} &= [ROT3(-\Omega)][ROT1(-i)][ROT3(-\omega)]\vec{r}_{PQW}
= \left [ \frac{IJK}{PQW} \right ]\vec{r}_{PQW}\\
\vec{v}_{IJK} &= [ROT3(-\Omega)][ROT1(-i)][ROT3(-\omega)]\vec{v}_{PQW}
= \left [ \frac{IJK}{PQW} \right ]\vec{v}_{PQW}\\
\end{align}
Previous rotations (3-1-3) can be expressed in terms of a single rotation matrix:
.. math::
\left [ \frac{IJK}{PQW} \right ]
.. math::
\begin{bmatrix}
\cos(\Omega)\cos(\omega) - \sin(\Omega)\sin(\omega)\cos(i) & -\cos(\Omega)\sin(\omega) - \sin(\Omega)\cos(\omega)\cos(i) & \sin(\Omega)\sin(i)\\
\sin(\Omega)\cos(\omega) + \cos(\Omega)\sin(\omega)\cos(i) & -\sin(\Omega)\sin(\omega) + \cos(\Omega)\cos(\omega)\cos(i) & -\cos(\Omega)\sin(i)\\
\sin(\omega)\sin(i) & \cos(\omega)\sin(i) & \cos(i)
\end{bmatrix}
Parameters
----------
k : float
Standard gravitational parameter (km^3 / s^2).
p : float
Semi-latus rectum or parameter (km).
ecc : float
Eccentricity.
inc : float
Inclination (rad).
omega : float
Longitude of ascending node (rad).
argp : float
Argument of perigee (rad).
nu : float
True anomaly (rad).
Returns
-------
r_ijk: np.array
Position vector in basis ijk
v_ijk: np.array
Velocity vector in basis ijk
"""
r_pqw, v_pqw = rv_pqw(k, p, ecc, nu)
r_ijk = transform(r_pqw, -argp, 2)
r_ijk = transform(r_ijk, -inc, 0)
r_ijk = transform(r_ijk, -raan, 2)
v_ijk = transform(v_pqw, -argp, 2)
v_ijk = transform(v_ijk, -inc, 0)
v_ijk = transform(v_ijk, -raan, 2)
return r_ijk, v_ijk