Inertia tensor(math snippet) (Q2052): Difference between revisions
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Added content item: Inertia tensor(math snippet) |
Added content item: Inertia tensor(math snippet) |
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| 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 | |||
\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 | |||
| 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 | |||
Normal rank | |||
| 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ | |||
| 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 | |||
Normal rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
Normal rank | |||
Revision as of 09:47, 7 October 2026
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inertia tensor(math snippet) |
No description defined |
Statements
\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
0 references
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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
0 references