Having one stable and one unstable equilibrium point would make impossibleĪn ellipse has two stable and two unstable points of equilibrium. There is a rigorous proof for this fact which shows that To do this, you'd have to flatten the end of theĮllipse out in some way, creating another stable equilibrium in the You can get some intuitionĪs to whay that is by trying to get rid of one of the unstableĮquilibrium points of the ellipse. That has just one stable and one unstable equilibrium point? TheĪnswer is 'no'. Uniform throughout without bulges or weights) Its long 'side' and two unstable ones at its ends.Ĭan you find a two-dimensional shape that is convex (it doesn'tīulge inwards) and homeogeneous (the material it's made of is

An ellipse, which is a bit like a length-wiseĬross-section of an egg, has two stable equilibria in the centres of Ones at the centres of its sides and three unstable ones at itsĬorners. A triangle has three of each, again three stable It also has four unstable equilibrium points at Stable equilibrium points, the centres of its sides: if you trap the squareīetween two vertical glass plates then you can balance it at those points. What combination of equilibrium points can an object have? It's easier to Points around the egg's body on which it balances robustly are called 'unstable' because the egg will fall over at the slightest nudge. 'Equilibrium' because you can balance the egg on them and The two tips of the egg are known as unstable equilibrium The slightest disturbance will make it topple With a lot of skill youĬan also balance it on one of its two ends: it's not easy and if you manage, You can nudge it,īut as long as you don't do it too hard it will settle down again. You can put it down on its side, it will rollĪround a little but eventually come to rest. So what are Gömböcs and what makes them special? Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all. Until quite recently, no-one knew whether Gömböcs even existed. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around with an apparent will of its own. In comparison to the two-dimensional analysis, there are more reasonable/cost-effective measures to increase the system stability through 3D analyses for several conditions (e.g., seismic loading).Your browser does not support the video tag.ĭirect link What's this? Read on to find out.Ī Gömböc is a strange thing. This formulation is applied to a valley landfill slope in China. This study proposes a practical way to track the irregular 3D tension cracking by repeating the analysis and excluding the columns with the negative normal forces at the bottom. The varication examples show: (i) the insensitivity of the FS to the prescribed functions in the MP assumption, (ii) the reliability of the method to cope with a complicated slope geometry (simplified methods may provide a larger FS for certain cases), and (iii) the superior efficiency of the algorithm (requires several seconds to converge). The numerical instability that is related to the different orders of magnitude for the residuals is avoided. Along with the recasting correction coefficients, they are solved with the triple nested algorithm. The advantage is that the unknowns of the different physical meanings (i.e., factor of safety (FS) and the coefficients in the MP assumption) are determined by balancing the forces and moments independently. The generalized 3D Morgenstern-Price's (MP) assumption for the intercolumn forces is recast into incremental forms. It satisfies six equilibrium conditions and includes all of the components of the intercolumnar forces. A new derivation of the three-dimensional (3D) limit equilibrium method for slope stability analyses is presented, which applies linear algebra operations to matrices to achieve a highly efficient algorithm while maintaining the rigorousness of the formulation.

Stable equilibrium 3d