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I have been dealing with the following differential equations:

[tex]

\frac{d \mathbf{m_1}}{dt} = \gamma_1 \mathbf{m_1} \times \mathbf{B} - \frac{n_{2}}{\gamma_{cr}} \mathbf{m_1} +

\frac{n_1}{\gamma_{cr}} \mathbf{m_2}

[/tex]

[tex]

\frac{d \mathbf{m_2}}{dt} = \gamma_2 \mathbf{m_2} \times \mathbf{B} - \frac{n_{1}}{\gamma_{cr}} \mathbf{m_2} +

\frac{n_2}{\gamma_{cr}} \mathbf{m_1}

[/tex]

The weird things is that [tex] \frac{d (\mathbf{m_1} + \mathbf{m_2})}{dt} [/tex] is not independent of [tex] \gamma_{cr} [/tex] even though when you add bottom and top deq's the [tex] \gamma_{cr} [/tex] terms cancel out. All I know is that it has something to do with [tex] \gamma_{1} \neq \gamma_{2} [/tex] .

Also when you convert to polar coordinates (i assume the m-vectors are only in the x-y direction and B is in the z-direction), the 2 diff. eq.'s take on a form where it's obvious that the [tex] \gamma_{cr} [/tex]'s stick around.

I'm not too fluent in differential equations so I'm not sure if there's an obvious answer here.

Thanks.