Inertia matrix(math snippet) (Q2052): Difference between revisions
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Added content item: Inertia tensor(math snippet) |
Updated the item for Inertia matrix(math snippet) from Special:Update |
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| label / en | label / en | ||
Inertia | Inertia matrix(math snippet) | ||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: \n\\mathbf{I}\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}\n / rank | |||
| Property / note | |||
| Property / note: with\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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
\\overline{I}(O,S)_B\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} | |||
| Property / LaTeX source: \\overline{I}(O,S)_B\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} / rank | |||
Normal rank | |||
| Property / note | |||
where $\\mathbf{I}(O,S)_B$ is the inertia tensor of object or system (S) according to cartesian coordinate system $B$ of 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\n\n$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ | |||
| Property / note: where $\\mathbf{I}(O,S)_B$ is the inertia tensor of object or system (S) according to cartesian coordinate system $B$ of 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\n\n$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank | |||
Normal rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
Normal rank | |||
Latest revision as of 12:19, 7 October 2026
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inertia matrix(math snippet) |
No description defined |
Statements
\\overline{I}(O,S)_B\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}
0 references
where $\\mathbf{I}(O,S)_B$ is the inertia tensor of object or system (S) according to cartesian coordinate system $B$ of 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\n\n$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
0 references