друг друга пердуна's Journal

чтобы не потерять, строятся сечения к орбитам действия SO(3) на R^3n

https://arxiv.org/abs/2002.03995

Elimination of parasitic solutions in theory of flexible polyhedra
I. Kh. Sabitov, D. A. Stepanov
(Submitted on 10 Feb 2020)
The action of the rotation group SO(3) on systems of n points in the 3-dimensional Euclidean space R3 induces naturally an action of SO(3) on R3n. In the present paper we consider the following question: do there exist 3 polynomial functions f1, f2, f3 on R3n such that the intersection of the set of common zeros of f1, f2, and f3 with each orbit of SO(3) in R3n is nonempty and finite? Questions of this kind arise when one is interested in relative motions of a given set of n points, i.e., when one wants to exclude the local motions of the system of points as a rigid body. An example is the problem of deciding whether a given polyhedron is non-trivially flexible. We prove that such functions do exist. To get a necessary system of equations f1=0, f2=0, f3=0, we show how starting by choice of a hypersurface in CPn−1 containing no conics, no lines, and no real points one can find such a system.