latom.utils.coc

@authors: Alberto FOSSA’ Giuliana Elena MICELI

Functions

coe2sv_vec(a, e, i, raan, w, ta, gm)	Change of Coordinates from Classical Orbital Elements to State Vector in body-centred inertial reference frame.
eq2per(raan, i, w)	Rotation matrix from inertial, body-centred equatorial reference frame to perifocal reference frame.
lat_long2cartesian(lat, long, r)	Transformation from latitude, longitude to cartesian coordinates.
per2eq(raan, i, w)	Rotation matrix from perifocal reference frame to inertial, body-centred equatorial reference frame.
per2eq_vec(xp, yp, vxp, vyp, raan, i, w)	Transformation from perifocal reference frame to inertial, body-centred equatorial reference frame.
polar2eq_vec(r, theta, u, v, raan, i, w)	Transformation from polar coordinates to inertial, body-centred equatorial reference frame.
polar2per_vec(r, theta, u, v)	Transformation from polar coordinates to perifocal reference frame.
rot1(t)	Elementary rotation matrix around X axis.
rot3(t)	Elementary rotation matrix around Z axis.

latom.utils.coc.rot1(t)

Elementary rotation matrix around X axis.

Parameters

t (float) – Rotation angle [rad]

Returns

r – 3x3 rotation matrix around X axis

Return type

ndarray

latom.utils.coc.rot3(t)

Elementary rotation matrix around Z axis.

Parameters

t (float) – Rotation angle [rad]

Returns

r – 3x3 rotation matrix around Z axis

Return type

ndarray

latom.utils.coc.eq2per(raan, i, w)

Rotation matrix from inertial, body-centred equatorial reference frame to perifocal reference frame.

Parameters

• raan (float) – Right Ascension of the Ascending Node [rad]

• i (float) – Inclination [rad]

• w (float) – Argument of Periapsis [rad]

Returns

q – 3x3 rotation matrix from equatorial to perifocal reference frames

Return type

ndarray

latom.utils.coc.per2eq(raan, i, w)

Rotation matrix from perifocal reference frame to inertial, body-centred equatorial reference frame.

Parameters

• raan (float) – Right Ascension of the Ascending Node [rad]

• i (float) – Inclination [rad]

• w (float) – Argument of Periapsis [rad]

Returns

q – 3x3 rotation matrix from perifocal to equatorial reference frames

Return type

ndarray

latom.utils.coc.coe2sv_vec(a, e, i, raan, w, ta, gm)

Change of Coordinates from Classical Orbital Elements to State Vector in body-centred inertial reference frame.

Parameters

• a (float) – Semi-major axis [m]

• e (float) – Eccentricity [-]

• i (float) – Inclination [rad]

• raan (float) – Right Ascension of the Ascending Node [rad]

• w (float) – Argument of Periapsis [rad]

• ta (ndarray) – True anomalies [rad]

• gm (float) – Central body standard gravitational parameter [m^3/s^2]

Returns

• r_vec (ndarray) – Position vector [m]

• v_vec (ndarray) – Velocity vector [m/s]

latom.utils.coc.polar2per_vec(r, theta, u, v)

Transformation from polar coordinates to perifocal reference frame.

Parameters

• r (ndarray) – Radius time series [m]

• theta (ndarray) – Angle time series [rad]

• u (ndarray) – Radial velocity time series [m/s]

• v (ndarray) – Tangential velocity time series [m/s]

Returns

• xp (ndarray) – Position along x axis [m]

• yp (ndarray) – Position along y axis [m]

• vxp (ndarray) – Velocity component along x axis [m/s]

• vyp (ndarray) – Velocity component along y axis [m/s]

latom.utils.coc.per2eq_vec(xp, yp, vxp, vyp, raan, i, w)

Transformation from perifocal reference frame to inertial, body-centred equatorial reference frame.

Parameters

• xp (ndarray) – Position along x axis [m]

• yp (ndarray) – Position along y axis [m]

• vxp (ndarray) – Velocity component along x axis [m/s]

• vyp (ndarray) – Velocity component along y axis [m/s]

• raan (float) – Right Ascension of the Ascending Node [rad]

• i (float) – Inclination [rad]

• w (float) – Argument of Periapsis [rad]

Returns

• r_vec (ndarray) – Position vector [m]

• v_vec (ndarray) – Velocity vector [m/s]

latom.utils.coc.polar2eq_vec(r, theta, u, v, raan, i, w)

Transformation from polar coordinates to inertial, body-centred equatorial reference frame.

Parameters

• r (nd array) – Radius time series [m]

• theta (ndarray) – Angle time series [rad]

• u (nd array) – Radial velocity time series [m/s]

• v (ndarray) – Tangential velocity time series [m/s]

• raan (float) – Right Ascension of the Ascending Node [rad]

• i (float) – Inclination [rad]

• w (float) – Argument of Periapsis [rad]

Returns

• r_vec (ndarray) – Position vector [m]

• v_vec (ndarray) – Velocity vector [m/s]

latom.utils.coc.lat_long2cartesian(lat, long, r)

Transformation from latitude, longitude to cartesian coordinates.

Parameters

• lat (float) – Latitude [deg]

• long (float) – Longitude [deg]

• r (float) – Planet radius [m]