{"entities":{"Q2052":{"pageid":4028,"ns":120,"title":"Item:Q2052","lastrevid":9230,"modified":"2026-10-07T12:19:55Z","type":"item","id":"Q2052","labels":{"en":{"language":"en","value":"Inertia matrix(math snippet)"}},"descriptions":{},"aliases":{},"claims":{"P1":[{"mainsnak":{"snaktype":"value","property":"P1","hash":"6056844c4a6d3699fbafab69805eed5ca36eab0e","datavalue":{"value":{"entity-type":"item","numeric-id":4,"id":"Q4"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q2052$58FEB9AD-9644-4DDB-BD8C-B21F73903CDD","rank":"normal"}],"P4":[{"mainsnak":{"snaktype":"value","property":"P4","hash":"e88f9a6969c48da04a7ccc7b410a5658d12695c3","datavalue":{"value":"\\\\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}","type":"string"},"datatype":"string"},"type":"statement","id":"Q2052$3102C3A8-23D4-412E-A011-56AFF6947AC7","rank":"normal"}],"P75":[{"mainsnak":{"snaktype":"value","property":"P75","hash":"64289e84f4a46707cb01ace2f7cfa1e4396f9b6b","datavalue":{"value":"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$$\\nI_{xy}=I_{yx}=-\\\\int_S xy\\\\,dm,\\\\qquad\\nI_{xz}=I_{zx}=-\\\\int_S xz\\\\,dm,\\\\qquad\\nI_{yz}=I_{zy}=-\\\\int_S yz\\\\,dm\\n$$","type":"string"},"datatype":"string"},"type":"statement","id":"Q2052$E157D8C8-66CB-4D24-ACFE-401315CE8CCE","rank":"normal"}],"P6":[{"mainsnak":{"snaktype":"value","property":"P6","hash":"d92372df44774f866200aa6fd16439ffabdc85d9","datavalue":{"value":{"entity-type":"item","numeric-id":147,"id":"Q147"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q2052$80D25477-5587-4037-BE16-18F4CFD9F87D","rank":"normal"}]},"sitelinks":{}}}}