I Time derivative of the angular momentum as a cross product

[AndersF]

I am trying to find the equations of motion of the angular momentum $\boldsymbol L$ for a system consisting of a particle of mass $m$ and magnetic moment $\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}$ in a magnetic field $\boldsymbol B$. The Hamiltonian of the system is therefore

$H=\frac{p^{2}}{2 m}-\gamma \boldsymbol{L} \cdot \boldsymbol{B}$

I have found that the time evolution equation for the angular momentum is

$\frac{d \boldsymbol{L}}{d t}=-\gamma \boldsymbol{B} \times \boldsymbol{L}$

However, the solution identifies the term $-\gamma \boldsymbol{B}$ with the angular velocity $\boldsymbol{\Omega}$:

$\frac{d \boldsymbol{L}}{d t}=\boldsymbol{\Omega} \times \boldsymbol{L}$

I do not understand what the justification is for making this identification. This last equation looks familiar to me, but I'm not sure where I've seen it... Could someone give me some guidance on this?

 

[anuttarasammyak]

I think he introduced a new parameter defined as
\Omega:=-\gamma B.

 

[AndersF]

Okay, but does the formula $\frac{d \boldsymbol{L}}{d t}=\boldsymbol{\Omega} \times \boldsymbol{L}$ have any special meaning, being $\boldsymbol{\Omega}$ the angular velocity?

 

[hutchphd]

https://en.wikipedia.org/wiki/Larmor_precession