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The inertia matrix explained


I'd like to find some documentation about the inertia matrix in Gazebo/ROS (this topic is located in between).

Here is the ROS wiki page:

Basically, what I do not understand, is that the inertia matrix could not be independent from the mass. How a discrepancy between a dummy inertia matrix and the real inertia matrix could impact the simulation?

Thanks in advance for any doc that could help me to understand this part of the robot models.