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→Derivation
b = magnetic field <br \>
From this equation, it is clear that the torque is maximized for m ⊥ b and that no torque is produced when m ∥ b. Another useful consideration for the development of a stabilizing control law is that the control torque has to be proportional to -, in order to decrease the kinetic energy of the object. <br \>
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, which instead of calculating the commanded magnetic moment with a proportional gain factor, uses the maximum torquer strength.