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Functions:

gravityEarth(r, m)

function F_G = gravityEarth(r, m)

Parameters:

Name	Datatype	Description
r	Vector	Vector pointing from the earth’s center to the location of the object.
m	Int	Mass of the object

Return:

Name	Datatype	Description
F_G	Vector	The force acting on the object by the gravitation of the earth.

Formular: F = G * m * m_Earth / r^2

Reference: https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#Modern_form

mFluxDesity(r, m)

function B = mFluxDesity(r, m)

Parameters:

Name	Datatype	Description
r	Vector	Vector pointing from the earth’s center to the location.
m	Vector	Magnetic dipole momentum of the magnet causing the magnetic field

Return:

Name	Datatype	Description
B	Vector	The flux-density at the location caused by the magnet.

Formular: B = mu_0 / (2 * PI) * ( 3 * r * (m * r) / |r|^5 - m / |r|^3 )

Reference: https://en.wikipedia.org/wiki/Magnetic_dipole#External_magnetic_field_produced_by_a_magnetic_dipole_moment

magneticForces(r, m, mE)

function F_m = magneticForces(r, m, mE)

Parameters:

Name	Datatype	Description
r	Vector	Vector pointing from the earth’s center to the location of the magnet.
m	Vector	Magnetic dipole momentum of the magnet which is watched.
mE	Vector	Magnetic dipole momentum of the earth.

Return:

Name	Datatype	Description
F_m	Vector	The force acting on the center of the magnet by the magnetic force of the earth.

Formular:

rh = r / norm(r);
F_m = 3 * MU_0 /( 4* pi * (norm(r)^4)) * ( m * dot(mE, rh) + mE * dot(m,r) + rh * dot(m, mE) - 5 * rh * dot(mE, rh) * dot(m, rh))

Reference: https://en.wikipedia.org/wiki/Magnetic_moment#Forces_between_two_magnetic_dipoles

magneticTorque(B, m)

function t = magneticTorque(B, m)

Parameters:

Name	Datatype	Description
B	Vector	Magnetic flux desitiy at the location of the object.
m	Vector	Magnetic dipole moment of the magent.

Return:

Name	Datatype	Description
t	Vector	The torque acting on the the magnet by the magnetic field of the earth.

Formular: t = m x B

Reference: https://en.wikipedia.org/wiki/Magnetic_moment#Forces_between_two_magnetic_dipoles

rotateVec(k, v, theta)

function vRot = rotateVec(k, v, theta)

Parameters:

Name	Datatype	Description
k	Unit Vector	Unit Vector describing the rotation axis.
v	Vector	Vector to be rotated around k.
theta	Double	Rotation angle in radiands.

Return:

Name	Datatype	Description
vRot	Vector	The rotated Vector.

Formular: vRot = v * cos(theta) + cross(k,v) * sin(theta) + k * dot(k,v) * (1 - cos(theta))

Reference: https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

solenoidDipoleMomentum(I, A)

function m = solenoidDipoleMomentum(I, A)

Parameters:

Name	Datatype	Description
I	Double	Current flowing through coil
A	Vector	Vector normal to the cross sectional area defining the magnitude

Return:

Name	Datatype	Description
m	Vector	The dipole momentum of the solenoid

Formular: m = COIL_TURNS * I * A * MU / MU_0

Reference: https://physics.stackexchange.com/questions/174988/magnetic-moment-of-an-iron-core-solenoid https://physics.stackexchange.com/questions/301655/dipole-moment-vector-of-solenoid-with-core?noredirect=1&lq=1

magneticTorqueSAT(posSAT, dirSAT, dirNormalSAT, I_1, I_2, I_3)

function t = magneticTorqueSAT(posSAT, dirSAT, dirNormalSAT, I_1, I_2, I_3)

Parameters:

Name	Datatype	Description
posSAT	Vector	Position vector to cubesat
dirSAT	Vector	Vector that describes the attitude of the cubesat
dirNormalSAT	Vector	Vector that describes the attitude of the cubesat
I_1	Double	Current through solenoid 1
I_2	Double	Current through solenoid 2
I_3	Double	Current through solenoid 3

Return:

Name	Datatype	Description
t	Vector	Resulting torque on the cubesat

Formular: t = magneticTorque(BSAT, magnetorquer1) + magneticTorque(BSAT, magnetorquer2) + magneticTorque(BSAT, magnetorquer3)

Reference: see above

getUsablity(v, u)

function c = getUsablity(v, u)

Parameters:

Name	Datatype	Description
v	Vector	Vector to be composed
u	Vector	Vector describing the axis

Return:

Name	Datatype	Description
c	Scalar with c >= 0	A measure for the ability to be controlled by the three magnetorquers

getComponent(v, u)

function c = getComponent(v, u)

Parameters:

Name	Datatype	Description
v	Vector	Vector to be composed
u	Vector	Vector describing the axis

Return:

Name	Datatype	Description
c	Scalar	The Component of the vector v along axis-vector u

getEstimatedDipoleMomentum(B, anglV, J)

function m = getDipoleMomentum(B, anglV, J)

Parameters:

Name	Datatype	Description
B	Vector	Vector describing the magnetic flux density at a predefined location
anglV	Vector	Vector describing the angular velocity of the cubesat
J	Matrix	Matrix-Representation of the satellite's moment of inertia

Return:

Name	Datatype	Description
m	Vector	The needed magnetic dipole moment for stabilization

Specific Constants

Earth Magnetic Dipole Moment:

|mEarth| ≈ 10^23  A*m²

http://rogerdudler.github.io/git-guide/