What are the Differences between Stable Unstable and Neutral Equilibrium

According to the ancient Greek philosopher Heraclitus, one cannot step into the same river twice. This expresses the fact that everything in the world is subject to change. Yet the Mississippi River may still be called the Mississippi River, so they must be something there that is unchanging, despite the flowing waters, the changing banks, the growing level of contamination etc.

The term equilibrium in physics is used to describe a similar concept. It is easily confused with stillness, or non-activity, but the term is never used without implying that there is continuing activity. The apparent non-activity is then explained as the balance of the various factors affecting the state of equilibrium so that they cancel each other out. A glass sitting on top of a wooden table is said to be in a state of equilibrium. The weight of the glass is supported by the frame of the table, which exerts an equal and opposite force to the weight (by Newton’s third law). If there is a gentle wind in the room, which isn’t strong enough to topple the glass, frictional forces of the table will be balancing the rotational moment exerted on the glass by the wind. In other words, there is a lot happening, but the glass remains stationary, and therefore it is in a state of equilibrium.

It should further be pointed out that the glass on the table is in a stable equilibrium. This implies that any slight change in the relevant forces that make up the equilibrium will not be enough to change the position of the glass. Pouring some water in the glass increases the weight, which is immediately counteracted upon by the table exerting a greater upward force. Trying to push the glass is resisted at first by friction. Slightly hinging it does not make it topple, and letting go makes it return to its original position.

Of course there are degrees of stability. You may easily push the glass to another position on the table. Therefore stability on the horizontal plane is not that good. Much better is the stability in the vertical plane. A great weight would need to be added for the glass to make a dent in the table, and nothing would make it go up. As far as toppling the glass, the stability is midway. A breeze is not enough, but a strong wind would certainly do it.

An ideal example of stable equilibrium will be a marble at the bottom of a perfectly round bowl. If the marble is moved in any direction it tends to come back to its original position. The same principle acts on the weight of a pendulum. It doesn’t matter that the weight will go on swinging forever if not for other dampening forces. The weight, in its stationary state, will still be said to be in a state of equilibrium, only because any effort to move it will be opposed.

Unstable equilibrium occurs when any slight change in position exacerbates the imbalance, pushing it further away from the state of equilibrium. A marble balanced on the summit of a hemisphere will be the perfect example. The equilibrium is obviously a precarious one. Even the slightest change in position will send the marble rolling all the way down.

Neutral equilibrium will fit in between both these extremes. A marble rolling on the table will serve as example. A slight impulse will send the marble rolling, but not drastically, and frictional forces will eventually bring it to rest. The pushing of the glass, as seen above, will not qualify. Frictional forces do actually oppose the original impulse, and therefore it remains in a stable equilibrium.

Stable equilibrium describes how, in a continuously changing world, there is still a regularity. Scientists discover the laws governing nature because these laws do not fall apart due to random and whimsical influences. The planets are in a stable equilibrium in their trajectories around the Sun, which eventually allowed Kepler to discover the planetary laws.

However, unstable equilibrium also has a vital role to play in the scheme of things. In the 18th century it was widely thought that everything in the world acts with clockwork regularity, by physical laws which allow for no equivocation. But uncertainty also plays its part in the world, something that eventually came to be enshrined in Heisenberg’s principle of uncertainty.

If something is in a state of unstable equilibrium, the slightest change, one way or the other, gives rise to huge differences in the end result. A marble perched on top of a round bowl may eventually fall in any direction. If one of those directions contains a detonator to a deadly bomb, the difference is between life and death. The study of unstable equilibrium has given rise to chaos theory, a key development in modern physics, and with huge relevance to real life systems. The central theme of chaos theory is graphically expressed through the butterfly effect. This is usually illustrated in the following way: “a mere flap of a butterfly’s wing in Brazil can set off a tornado in Texas”. It expresses the unimaginable complexity of the Earth’s ecosystem, in which unstable equilibrium plays a significant role.