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- W3032928607 abstract "The action of the rotation group $SO(3)$ on systems of $n$ points in the $3$-dimensional Euclidean space $mathbf{R}^3$ induces naturally an action of $SO(3)$ on $mathbf{R}^{3n}$. In the present paper we consider the following question: do there exist $3$ polynomial functions $f_1$, $f_2$, $f_3$ on $mathbf{R}^{3n}$ such that the intersection of the set of common zeros of $f_1$, $f_2$, and $f_3$ with each orbit of $SO(3)$ in $R^{3n}$ 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 $f_1=0$, $f_2=0$, $f_3=0$, we show how starting by choice of a hypersurface in $mathbf{CP}^{n-1}$ containing no conics, no lines, and no real points one can find such a system." @default.
- W3032928607 created "2020-06-12" @default.
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- W3032928607 date "2020-06-01" @default.
- W3032928607 modified "2023-10-08" @default.
- W3032928607 title "Elimination of parasitic solutions in the theory of flexible polyhedra" @default.
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- W3032928607 doi "https://doi.org/10.1007/s13366-020-00503-w" @default.
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