Julián Ascolani Yael Is the starting point a finite element model?

The inertia tensor is a function of several geometric and material parameters. If they are assumed as random variables following a certain PDF, it should be possible - in principle - to compute the PDF of the inertia tensor in closed form by applying transformation formulas of random variables

Nils Wagner , thank you for your reply. I'd say yes, it is, but I don't have access to this model. I get the mean values and deviations of mass and elements of the inertia tensor as inputs, so I can't access the information of the mass density. I am trying to think whether it is possible to reduce the dimensions of the parameter space I have to explore to consider all the uncertainties.

Julián Ascolani Yael What is the ultimate goal of the investigation? Is it about optimizing the inertia properties?

Denis Benasciutti , this sounds interesting. I am exploring this now. I am not sure I'll be able to relate CoM with Inertias without having an explicit expression (or numerical) of PDF of the mass density, I guess this might bring me some difficulties.

Nils Wagner. I need to estimate how the uncertainties in the Center of Mass and Inertia tensor affect the equations of motion. I plan to perform a Monte Carlo simulation. But, since I have many degrees of freedom and the simulations are not very fast, I am exploring the possibility of reducing the degrees of freedom to reduce the computational cost a little.

The relationship between uncertainty in the center of mass and uncertainties in the inertia tensor can be understood through the concepts of moment of inertia and dynamics. The inertia tensor is a mathematical representation of an object's distribution of mass, providing information about how mass is distributed relative to different axes. It is a crucial component in understanding an object's rotational behavior. Uncertainty in the center of mass refers to the degree of error or lack of precision associated with determining the exact location of an object's center of mass. In physics, when considering uncertainties, it is essential to take into account how uncertainties propagate through different physical quantities. This principle can be applied to relate uncertainty in the center of mass to uncertainties in the inertia tensor. If there are measurement uncertainties or errors associated with determining an object's center of mass, these uncertainties will impact calculations involving moments of inertia and rotational dynamics. In particular, if there are inaccuracies in locating the exact position of an object's center of mass, this can lead to errors when calculating moments on some axis rotationally leading towards changes produced due to inaccurate knowledge about distribution brought up by miscalculating inertia tensors leading towards errors made within various calculated vectors like angular momentum or taking action from torque applied using inaccurate data that has been gathered concerning these entities bringing change within decision-making processes (cause effect relationship) resulting for instance from measuring quantities such as torque not being what they should have been yielding incorrect outcome based on those inaccuracies. This issue highlights accurate determination and reduction uncertainty regarding a body’s centre-of-mass position are critical for precise calculation involving rotational dynamics and moments (or torques) as imprecise information might give wrong results causing cascading problems down line given their interconnected nature more so particularly when they rely one upon other given relationships such as spatial arrangements between various components making up system under consideration becoming inclusive part rather than exclusive factor influencing decisions made within framework used its functionality over time .