- #1
BeauGeste
- 49
- 0
I'm not sure where to put this but I though DEQ would be a good start.
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.
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.