# Inertia Tensor of the "Tetra" shape class

Hi,

I think I have spotted a mistake in the calculation of the Inertia Tensor for the "Tetra" shape class (since the day calls for inertia-related amendments :) ). In the Tetra.cpp script, the Inertia Tensor is calculated exactly as in [1]. The thing is, this paper has a typo, and although the non-diagonal inertia values "a', b', c'" (stated in the source code as: "a__ , b__ , c__") are calculated correctly, their position in the Inertia tensor seems to be false. In particular, the terms "-b__" and "-c__" should be in each other's place, since these terms are defined as:

b' (=b__) term: $$b' = \int_{D} μ*x*z dD $$ : Involving x-z coordinates: should be present in the (0,2) (2,0) cells of the tensor

c' (=c__) term: $$c' = \int_{D} μ*x*y dD $$ : Involving x-y coordinates: should be present in the (0,1) (1,0) cells of the tensor

I see this has also been spotted in the Polyhedra_

Matrix3r ret; ret<<

a , -c__, -b__,

-c__, b , -a__,

-b__, -a__, c ;

return ret;

## Question information

- Language:
- English Edit question

- Status:
- Solved

- For:
- Yade Edit question

- Assignee:
- No assignee Edit question

- Solved by:
- Robert Caulk

- Solved:
- 2019-04-24

- Last query:
- 2019-04-24

- Last reply:
- 2019-04-24

Robert Caulk (rcaulk) said : | #1 |

Thanks for spotting this, it looks like you are right (I guess you are referring to these lines in particular [1][2]). Do you want to go ahead and make a merge request on GitLab? Or shall I?

[1]https:/

[2]https:/

Thanks for checking this Robert!

Yes, I refer to the lines you sent.

Just made a merge request on GitLab.

Many thanks,

Vasileios

Thanks Robert Caulk, that solved my question.