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→Derivation
The b-dot control law takes advantage of the fact that the derivative of the magnetic field vector is both perpendicular to b and proportional to ω, hence the commanded magnetic dipole can be expressed as: <ref>https://www.researchgate.net/publication/263008407_Comparison_of_Control_Laws_for_Magnetic_Detumbling</ref> <br \>
[[File:Equation56.gif|frame|center]]
There are multiple variations of the B-dot control law, like the B-dot bang-bang controller<ref>http://www.diva-portal.org/smash/get/diva2:1018210/FULLTEXT02.pdf </ref>, which instead of calculating the commanded magnetic moment with a proportional gain factor, uses the maximum torquer strength.
[[File:Equation57.gif|frame|center]]
Details on the other types of B-Dot control laws which can be used to control the satellite during detumbling can be found [http://www.diva-portal.org/smash/get/diva2:1018210/FULLTEXT02.pd here].