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Coriolis field : ウィキペディア英語版
Coriolis field

In theoretical physics a Coriolis field is one the ''apparent'' gravitational fields felt by a rotating or forcibly-accelerated body, together with the centrifugal field and the Euler field.
==Mathematical expression==

Being \vec\omega is the angular velocity vector of the rotating frame, \vec v the speed of a test particle used to measure the field, and using the expression of the acceleration in a rotating reference frame, it is known that the acceleration of the particle in the rotating frame is:
:
\mathbf__ -
\boldsymbol\omega \times (\boldsymbol\omega \times \mathbf) -
\frac \times \mathbf

the Coriolis force is assumed to be the fictitious force that compensates the second term:
:
\mathbf_) =
-2 ( \boldsymbol\omega \times \mathbf)

Where \vec p denotes the linear momentum. It can be seen that for any object, the coriolis force over it is proportional to its momentum vector. As vectorial product can be expressed in a tensorial way using the Hodge dual of \omega:
:\mathbf_ \times \mathbf) = -2(\mathbf \times) \mathbf = \begin\,0&\!-2\omega_3&\,\,2\omega_2\\ \,\,2\omega_3&0&\!-2\omega_1\\-2\omega_2&\,\,2\omega_1&\,0\end\beginp_1\\p_2\\p_3\end
This matrix can be seen as a constant tensor field, defined in the whole space, that will yield coriolis forces when multiplied by momentum vectors.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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