These are very interesting questions! There's a useful concept of stability that's based on considering what happens under an arbitrarily small perturbation. Omitting mention of physics, we can define * for any set R = {r_j | j in J} of radii r_j > 0 (where J is some index set) with finite sum Sum_{j in J} r_j, let disk D_j in the plane have radius r_j. * Define an arrangement A = {D_j} in the plane of non-overlapping disks D_j in the plane, where the radius of D_j is r_j. This means that for each D_j, A is a choice of *center* = c_j in R^2. Non-overlapping means that for each pair of indices j ≠ k, we have ||c_j - c_k|| >= r_j + r_k. * Let D(A) be the smallest disk in R^2 containing each D_j in its interior. Then define diam(A) = diameter(D). * For an arrangement A and eps > 0, define an *eps-close perturbation* of A to be an arrangement A' with the same radii r_j but with each center c_j replaced by a new center c'_j, such that the sum of the center discrepancies ||c_j - c'_j|| is bounded above by eps: Sum_{j in J} ||c_j - c'_j|| < eps. * Finally, say an arrangement A is *stable* if there exists eps > 0 such that every eps-close perturbation A' of A satisfies diam(A') >= diam(A). In other words, small perturbations to A cannot decrease diam(A). —Dan ----- ... ... Is there a ... multiset of diameters ... that cannot be bungee-bundled, in the sense that for any stable way of wrapping them circumferentially with an elastic cord, there’ll be a rattler? My notion of stability is based on the assumption that the (potential) energy of the system is the length of the cord; I assume that energy cannot increase, that there is no slippage between rolls, and that there is no slippage between the bungee cord and the rolls that it touches. ... PS: Maybe my attempted formalization of the notion of stability needs some improvement. I think that the 1,epsilon,1 shishkebab is technically stable because of the no-slip conditions, but this doesn’t correspond to physical reality. -----