I always had trouble envisioning this. I think part of the reason is the "angle x", which, according to the explanation and video on this page, is vector-valued, not scalar. IVT applies to scalar functions, is there an equivalent for a function with a vector domain?
The table does not rotate around its own axis, but rather it rotates in "such a way that three legs stay on the surface", i.e. moves around in 3d with a surface-contact constraint, which seems like a motion with more than one degree of freedom to me. Is such a rotation always possible? Is the motion somehow effectively 1D?
These questions don't seem to have "obvious" answers to me, and they're only addressed as "assumptions" on this page.
The table does not rotate around its own axis, but rather it rotates in "such a way that three legs stay on the surface", i.e. moves around in 3d with a surface-contact constraint, which seems like a motion with more than one degree of freedom to me. Is such a rotation always possible? Is the motion somehow effectively 1D?
These questions don't seem to have "obvious" answers to me, and they're only addressed as "assumptions" on this page.