“inertia matrix”的概念、定义、翻译、参考文献-科学参考

inertia matrix

Mathematics

The inertia matrix (or inertia tensor) I_P of a rigid body (associated with a given point P) arises in the calculation of the kinetic energy and the angular momentum of the body in general motion. It is the symmetric matrix

$I_{P} = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{x y} & I_{y y} & I_{y z} \\ I_{x z} & I_{y z} & I_{z z} \end{matrix}]$

(see moment of inertia, product of inertia). By the spectral theorem, there is an orthogonal set of axes—the principal axes—with respect to which the inertia matrix is diagonal with the diagonal entries being the principal moments of inertia.

单词	inertia matrix
释义	inertia matrix Mathematics The inertia matrix (or inertia tensor) I_P of a rigid body (associated with a given point P) arises in the calculation of the kinetic energy and the angular momentum of the body in general motion. It is the symmetric matrix $I_{P} = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{x y} & I_{y y} & I_{y z} \\ I_{x z} & I_{y z} & I_{z z} \end{matrix}]$ (see moment of inertia, product of inertia). By the spectral theorem, there is an orthogonal set of axes—the principal axes—with respect to which the inertia matrix is diagonal with the diagonal entries being the principal moments of inertia.
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