Calculating/simulating effect of mass changes in a gyroscope

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Free software options for simulating gyroscope behavior with mass changes are sought due to the complexity of manual calculations. The discussion highlights the differing behaviors of gyroscopes in various environments, such as on the ground versus in free fall. A specific example is provided regarding smartphone gyroscopes, which can vibrate due to misbalanced mass when rotating. Questions arise about the effects of free fall on the gyroscope's mass and rotation dynamics. The conversation emphasizes the need for formulas to aid in developing a simulation program.
jumpjack
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Can anybody suggest a free SW to simulate the behavior of a gyroscope upon adding/removing a mass in various places with respect its rotational axis and/or baricenter? It looks like it's quite complex to manually calculate or just "imagine" it.

A gyro standing on a floor does behave in a different manner from a gyro floating in free space or from one freely falling down.

For example, in our smartphone there is a little "gyroscope" with a misbalanced mass which, upon rotation, causes a vibration (=attempt to put the baricenter on the rotation axis); but what would happen to the phone while freely falling? Would it vibrate, or would the mass start rotating around its baricenter? (maybe not, because its controlling motor is in fixed position wrt the phone).
 
Maybe I could write by myself such a SW, but I need some hints about the formulas.
 

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