Item:Q2052 - Revision history

Rongzhou: Updated the item for Inertia matrix(math snippet) from Special:Update

2026-10-07T12:19:55Z

Updated the item for Inertia matrix(math snippet) from Special:Update

← Older revision		Revision as of 12:19, 7 October 2026
Property / instance of
	~~mathematical expression~~
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 $\\mathbf{I}(O,S)$ 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 $\\mathbf{I}(O,S)$ 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
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		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
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Updated the item for Inertia matrix(math snippet) from Special:Update

2026-10-07T12:15:49Z

Updated the item for Inertia matrix(math snippet) from Special:Update

← Older revision		Revision as of 12:15, 7 October 2026
Property / instance of
	~~mathematical expression~~
Property / instance of: mathematical expression / rank
	~~Normal rank~~
Property / LaTeX source
	~~\\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}~~
Property / LaTeX source: \\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} / rank
	~~Normal rank~~
Property / note
	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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
Property / note: 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank
	~~Normal rank~~
Property / attributed to
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		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 $\\mathbf{I}(O,S)$ 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 $\\mathbf{I}(O,S)$ 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
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Updated the item for Inertia matrix(math snippet) from Special:Update

2026-10-07T12:08:47Z

Updated the item for Inertia matrix(math snippet) from Special:Update

← Older revision		Revision as of 12:08, 7 October 2026
label / en		label / en
	Inertia ~~tensor~~(math snippet)		Inertia matrix(math snippet)
Property / instance of
	~~mathematical expression~~
Property / instance of: mathematical expression / rank
	~~Normal rank~~
Property / LaTeX source
	~~\\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}~~
Property / LaTeX source: \\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} / rank
	~~Normal rank~~
Property / note
	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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
Property / note: 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank
	~~Normal rank~~
Property / attributed to
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		Property / instance of: mathematical expression / rank
			Normal rank
		Property / LaTeX source
			\\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}
		Property / LaTeX source: \\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} / rank
			Normal rank
		Property / note
			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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
		Property / note: 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank
			Normal rank
		Property / attributed to
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Updated the item for Inertia tensor(math snippet) from Special:Update

2026-10-07T12:08:25Z

Updated the item for Inertia tensor(math snippet) from Special:Update

← Older revision		Revision as of 12:08, 7 October 2026
Property / instance of
	~~mathematical expression~~
Property / instance of: mathematical expression / rank
	~~Normal rank~~
Property / LaTeX source
	~~\\mathbf{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}~~
Property / LaTeX source: \\mathbf{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} / rank
	~~Normal rank~~
Property / note
	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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
Property / note: 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank
	~~Normal rank~~
Property / attributed to
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		Property / instance of: mathematical expression / rank
			Normal rank
		Property / LaTeX source
			\\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}
		Property / LaTeX source: \\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} / rank
			Normal rank
		Property / note
			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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
		Property / note: 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank
			Normal rank
		Property / attributed to
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Updated the item for Inertia tensor(math snippet) from Special:Update

2026-10-07T09:49:56Z

Updated the item for Inertia tensor(math snippet) from Special:Update

← Older revision		Revision as of 09:49, 7 October 2026
Property / instance of
	~~mathematical expression~~
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
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		Property / instance of: mathematical expression / rank
			Normal rank
		Property / LaTeX source
			\\mathbf{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}
		Property / LaTeX source: \\mathbf{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} / rank
			Normal rank
		Property / note
			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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$
		Property / note: 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$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$ / rank
			Normal rank
		Property / attributed to
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Added content item: Inertia tensor(math snippet)

2026-10-07T09:47:44Z

Added content item: Inertia tensor(math snippet)

← Older revision		Revision as of 09:47, 7 October 2026
Property / instance of
	~~mathematical expression~~
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
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		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
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Added content item: Inertia tensor(math snippet)

2026-10-07T09:47:44Z

Added content item: Inertia tensor(math snippet)

Show changes