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How can I calculate inertia tensor of composite shape. I have done math of moment of inertia, but not inertia tensor.

Can anyone help me with the calculation of this shape :

inertia of composite shape

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enter image description here

you can use the parallel axes theory :

$$I=I_1+I_2+I_3-m_1 \,\tilde{r}_{01}\,\tilde{r}_{01}-m_3\,\,\tilde{r}_{03}\,\tilde{r}_{03}$$

where :

$$\tilde{r}_{01}=\begin{bmatrix} 0 & -z & 0 \\ z & 0 & 0 \\ 0 & 0 & 0 \\ \end{bmatrix}$$

and $$\tilde{r}_{03}=\begin{bmatrix} 0 & +z & 0 \\ -z & 0 & 0 \\ 0 & 0 & 0 \\ \end{bmatrix}$$

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  • $\begingroup$ what are the value of $I_x$ and $I_y$ ? $\endgroup$ – Maifee Ul Asad Sep 29 '19 at 11:38
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    $\begingroup$ Sorry for that The result is I which is the inertia tensor $3\times3$ symmetric matrix $\endgroup$ – Eli Sep 29 '19 at 14:00
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    $\begingroup$ I took the * out , the result is the same as the first version. $\endgroup$ – Eli Sep 29 '19 at 20:25
  • $\begingroup$ Can you take a look here, please .. $\endgroup$ – Maifee Ul Asad Sep 30 '19 at 17:06
  • $\begingroup$ if I translate and move the whole object downward and then calculate the inertia tensor, what will be changed. I want to put the plane on the center of origin. I'm confused with those +/- signs. @Eli $\endgroup$ – Maifee Ul Asad Oct 24 '19 at 10:28

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