Reference solution
=====================

Calculation method
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Mass and center of gravity:

:math:`\begin{array}{}m=\rho \underset{v}{\int }\mathrm{dv}=\rho \underset{v}{\int }\mathrm{dx.dy.dz}\\ {x}_{G}=\frac{\underset{v}{\int }\mathrm{x.dv}}{m}{y}_{G}=\frac{\underset{v}{\int }\mathrm{y.dv}}{m}{z}_{G}=\frac{\underset{v}{\int }\mathrm{z.dv}}{m}\end{array}`

Inertia tensor:

:math:`\begin{array}{cc}{I}_{\mathrm{xx}}=\rho \underset{v}{\int }(\mathrm{y²}+\mathrm{z²})\mathrm{.}\mathrm{dv}& {I}_{\mathrm{xy}}=\rho \underset{v}{\int }\mathrm{x.y.dv}\\ {I}_{\mathrm{yy}}=\rho \underset{v}{\int }(\mathrm{x²}+\mathrm{z²})\mathrm{.}\mathrm{dv}& {I}_{\mathrm{xz}}=\rho \underset{v}{\int }\mathrm{x.z.dv}\\ {I}_{\mathrm{zz}}=\rho \underset{v}{\int }(\mathrm{x²}+\mathrm{y²})\mathrm{.}\mathrm{dv}& {I}_{\mathrm{yz}}=\rho \underset{v}{\int }\mathrm{y.z.dv}\end{array}`


Reference quantities and results
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Masses and inertias for the various models.


Uncertainty about the solution
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**Note:**

For one of the meshes modelled in shells, the solution is numerical (not regression).