Ad
related to: stable vs unstable equilibrium physics examplesstudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
The simplest kind of an orbit is a fixed point, or an equilibrium. If a mechanical system is in a stable equilibrium state then a small push will result in a localized motion, for example, small oscillations as in the case of a pendulum. In a system with damping, a stable equilibrium state is moreover asymptotically stable. On the other hand ...
For example, the function / (defined as 0 in x=0) has all derivatives equal to zero. At the same time, this function has a local minimum in x=0, so it is a stable equilibrium. If this function is multiplied by the Sign function, all derivatives will still be zero but it will become an unstable equilibrium.
A typical example of a differential equation with a saddle-node bifurcation is: = +. Here is the state variable and is the bifurcation parameter.. If < there are two equilibrium points, a stable equilibrium point at and an unstable one at +.
A ball located at this point, ball 3, is in equilibrium but unstable; the slightest disturbance will cause it to move to one of the stable points. Light switch, a bistable mechanism. In a dynamical system, bistability means the system has two stable equilibrium states. [1] A bistable structure can be resting in either of two states.
In a dynamical system, multistability is the property of having multiple stable equilibrium points in the vector space spanned by the states in the system. By mathematical necessity, there must also be unstable equilibrium points between the stable points.
A metastable state of weaker bond (1), a transitional "saddle" configuration (2) and a stable state of stronger bond (3). In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability.
In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if x e {\displaystyle x_{e}} is Lyapunov stable and all solutions that start out near x e {\displaystyle x_{e}} converge to x e {\displaystyle x_{e}} , then x e {\displaystyle x_{e}} is said to be asymptotically ...
For example, if the bowl containing a rolling marble was inverted and the marble was balanced on top of the bowl, the center bottom (now top) of the bowl is a fixed state, but not an attractor. This is equivalent to the difference between stable and unstable equilibria. In the case of a marble on top of an inverted bowl (a hill), that point at ...