Suppose I take a water bottle and impart two angular velocities on it simultaneously, i.e.

1)along the axis of the bottle

2)of the axis of the bottle itself about another axis perpendicular to it

what I see is not a simple rotation of the bottle along a third axis (in the direction of the diagonal of the parallelogram created by rotation "vectors" 1 and 2) but rather a complicated kind of motion. But then isn't this a contradiction to the kind of treatment we see in textbooks? Or is it any kind of a tensor? (PS: I don't have any advanced physics background but am somewhat well informed about the basic stuff)

Suppose I take a water bottle and impart two angular velocities on it simultaneously, i.e.

1. along the axis of the bottle

2. of the axis of the bottle itself about another axis perpendicular to it

what I see is not a simple rotation of the bottle along a third axis (in the direction of the diagonal of the parallelogram created by rotation "vectors" 1 and 2) but rather a complicated kind of motion. But then isn't this a contradiction to the kind of treatment we see in textbooks? Or is it any kind of a tensor? (PS: I don't have any advanced physics background but am somewhat well informed about the basic stuff)