B Dot Algorithm Overview

The principle of the B dot algorithm relies on the usage of magnetorquers to generate a torque opposite to the "natural" rotation of the satellite.

• We generate this torque by applying an alternating current (AC) to the coil in order to generate a magnetic moment.
  • if you are unfamiliar with AC, it simply means our current is continuously alternating between positive and negative current

This algorithm aims to reduce the angular speed.

Using the actuators

We generate a torque using the law as follows:

• $\overrightarrow{M}$ is the magnetic moment of the dipole (magnetorquer coil)
• $\overrightarrow{B}$ is the Earth's magnetic field
• $\theta$ is the angle between M and B
• $\overrightarrow{u}$ is the unit vector resulting from the cross product between M and B.

Note that T, Torque, is at a maximum when M and B are orthogonal (perpendicular).

This will help us minimize the angle between the coil's magnetic moment and the earth's magnetic field.

We can get the magnetorquer moment using the following equation:

• i is the intensity of the current flowing through one magnetorquer, in Amperes (A).
• n is the number of coils in the magnetorquer
• S is the surface enclosed by a turn of the coil's spiral (in metres squared, $m^2$).