id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_uo46qeedczcwnkv7pudgqqgyqa	P.L. Varkonyi	Static Equilibria of Rigid Bodies: Dice, Pebbles, and the Poincare-Hopf Theorem	2006	27	.pdf	application/pdf	10610	1369	82	classes are non-empty in the case of three-dimensional bodies; in particular we prove even more special class of bodies with just one stable and one unstable equilibrium (and . .) contains all homogeneous, convex, two-dimensional bodies with i stable and i unstable equilibria. . .) contains all homogeneous, convex bodies with i stable equilibria (minima) and j unstable equilibria (maxima). As demonstrated in [1], nondegenerated stable/unstable equilibria of the body correspond to local minima/maxima of R(ϕ). Before we identify suitable ranges of the parameters where the corresponding body B is convex and mono-monostatic (Section 4), let us briefly comment with only two static equilibria, so homogeneous, convex, mono-monostatic bodies exist point: section of B in the G S0 S1 plane, where G denotes the center of gravity of the body. suggests that all convex, homogeneous bodies have at least two stable equilibria and	./cache/work_uo46qeedczcwnkv7pudgqqgyqa.pdf	./txt/work_uo46qeedczcwnkv7pudgqqgyqa.txt