Inertia tensor(math snippet) (Q2052)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inertia tensor(math snippet) |
No description defined |
Statements
\\overline{I}(O,S)\n=\n\\begin{pmatrix}\nI_{xx} & I_{xy} & I_{xz}\\\\\nI_{yx} & I_{yy} & I_{yz}\\\\\nI_{zx} & I_{zy} & I_{zz}\n\\end{pmatrix}
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where $\\mathbf{I}(O,S)$ is the inertia tensor of object or system (S) according to cartesian coordinate system origin $O$ \n\nwith\n\n$$\nI_{xx}=\\int_S (y^2+z^2)\\,dm,\\qquad\nI_{yy}=\\int_S (x^2+z^2)\\,dm,\\qquad\nI_{zz}=\\int_S (x^2+y^2)\\,dm\n$$\n\nand off-diagonal terms\n\n$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
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