{"type":"rich","version":"1.0","title":"Inertia matrix(math snippet)","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"\\overline{I}(O,S)_B\n=\n\\begin{pmatrix}\nI_{xx} &amp; I_{xy} &amp; I_{xz}\\\\\nI_{yx} &amp; I_{yy} &amp; I_{yz}\\\\\nI_{zx} &amp; I_{zy} &amp; I_{zz}\n\\end{pmatrix}\">\\overline{I}(O,S)_B\n=\n\\begin{pmatrix}\nI_{xx} &amp; I_{xy} &amp; I_{xz}\\\\\nI_{yx} &amp; I_{yy} &amp; I_{yz}\\\\\nI_{zx} &amp; I_{zy} &amp; I_{zz}\n\\end{pmatrix}</span><div class=\"wb-embed-note\"><p>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</p><p>with\n</p><p>$$\nI_{xx}=\\int_S (y^2+z^2)\\,dm,\\qquad\nI_{yy}=\\int_S (x^2+z^2)\\,dm,\\qquad\nI_{zz}=\\int_S (x^2+y^2)\\,dm\n$$\n</p><p>and\n</p><p>$$\nI_{xy}=I_{yx}=-\\int_S xy\\,dm,\\qquad\nI_{xz}=I_{zx}=-\\int_S xz\\,dm,\\qquad\nI_{yz}=I_{zy}=-\\int_S yz\\,dm\n$$\n</p></div><footer><cite class=\"wb-embed-author\">Rong Martin-Siebler ZHOU</cite></footer>","width":640,"height":320}