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Definition of custom intertia properties in SimMechanics

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Jakub
Jakub 2012-7-3
关闭： MATLAB Answer Bot 2021-8-20
Dear support,
I want to define custom inertia properties in my SimMechanics-model. I am not quite sure if the terms "Moments of Inertia" and "Products of Inertia" are used in a correct way in the SimMechanics documentation. At least it is not explained clearly what the user is supposed to fill in the dialogue box.
From my CAD-modell I derived an inertia tensor in the form:
[J_11 J_12 J_13
J_12 J_22 J_23
J_13 J_23 J_33]
I use exactly the same coordinate system in my SimMechanics-model to make the import of data easier. The coordinate systems of imported stl-file is taken as the reference frame in SimMechanics. It is neither a principal coordinate system nor the origin is located at the centre of mass.
In this post Arnaud Miege says that inertia is defined relative to the centre of mass:
"The key parameters for a SimMechanics Body block are its mass and inertia tensor relative to the centre of gravity of the body."
I doubt that. It makes more sense to me when the inertia properties are relative to the reference frame.
My question is: What am I expected to fill in for "Moments of Inertia" and "Products of Inertia"?
The documentation which can be found in the link below says the following:
Documentation: Inertia
Quote:
Moments of Inertia
Enter the principal moments of inertia as a 3-vector in the frame R of the solid. In the drop-down list, choose units. The default is kg*m^2 (kilograms-meters2).
Products of Inertia
Enter the products of inertia as a 3-vector in the frame R of the solid. In the drop-down list, choose units. The default is kg*m^2 (kilograms-meters2).
Principal moments are not equal to J_11, J_22, J_33 in the general case. Does this mean that I have to derive the principal moments of inertia from my inertia matrix (which are the eigenvalues)? If this is the case: In which order do I have to list the principal moments in the dialogue box (Can be found under the point "Custom Inertia" in the doc.).
I guess that the products of inertia are equal to J_12, J_13, J_23. Again: In which order do I have to put the values into the vector required in the dialogue box?
In that respect the documantation page I referred to says:
Quote:
"The products of inertia are (I23, I13, I12)."
Is this the right order?
I am a bit confused that there does not seem to be a simple way to get my inertia tensor directly into SimMechanics. It is a problem of conventions.
I hope you can help and clarify what I need to fill in the dialogue box.
I apologize for my limited English writing skills as I am not a native speaker.
Kind regards.
Jakub

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回答（2 个）

Pouya Jamali
Pouya Jamali 2012-11-27
Diagonal elements of the inertia tensor are moments of inertia and the others are products of inertia. You should consider that this matrix is symmetrical so it just has 6 independent elements. If you have a CAD model it's better to use smlink to import the geometry automatically instead of fill in the inertia of the model parts manually.
Jakub
Jakub 2012-11-27
Thanks for your answer.
I know that the matrix is symmetric. I wrote the matrix down in Matlab Code at the beginning of my lengthy question. Here it is again:
[J_11 J_12 J_13
J_12 J_22 J_23
J_13 J_23 J_33]
The questions remain: What am exactly I supposed to fill in into the fields when I have the inertia tensor relative the centre of mass of a body? And which is the coordinate system the filled in moments and products of inertia need to refer to? It is either a coordinate system located at the centre of mass or the reference frame I guess.
I need to fill in the inertia properties manually because the CAD model is not complete.

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