I posted this question earlier in physics.stackexchange, but I think this is actually the best place for it.
I’m not familiar with sensor hardware, and I don’t really know how an accelerometer works. But I do know that from a mathematical point of view, you wouldn’t be able to uniquely determine the orientation of a solid object knowing only the acceleration of one of its points.
Indeed, assuming known initial conditions and acceleration function of one point, say point X, one can solve the second order ODE and get the position function for that point, but that wouldn’t determine the position of the rest of the points in the solid object, because the object could perform a rotation centered on point X, leaving it unchanged. Despite all that, I have seen several claims that modern mobile phones benefit from the inclusion of accelerometer sensor in such a way that enables them to, for example, determine the orientation of the screen. I don’t understand how an IPhone would know to what position the screen was tilted. Consider the following example where the red dot indicates the location of the accelerometer sensor.
Suppose acceleration data was processed and the motion of the sensor was determined as the red arc shown in the pictures below. How one could distinguish from the two depicted motions? Notice that the final orientation of the device is different.
Please note that by one accelerometer, I mean one that would be able to register accelerations in all 3 dimensions. That way, upon integration I would get the spacial (3D) trajectory of the point. I believe the issue I describe here holds even in such scenario.
Thanks for reading!