Stability of Equilibrium

Stability of Equilibrium

 

The equilibrium of a mechanical system is stable if after a small perturbation (displacement or push) the points of the system forever afterward differ but little from their equilibrium positions; otherwise, the equilibrium is unstable. Ordinarily with small perturbations, the points of a system in stable equilibrium will perform small oscillations around their equilibrium positions; in time the oscillations are damped by resistances, so that equilibrium is reestablished. The stability of equilibrium is defined and analyzed more rigorously in the same manner as the stability of motion. For a conservative mechanical system, the sufficient condition of the stability of equilibrium is that the potential energy of the system is minimal in the equilibrium state.

References in periodicals archive ?
Only afterwards we can analyze the Hamiltonian function in the neighborhood of each equilibrium configuration and investigate the stability of equilibrium positions (see [14,15,16]).
He covers the evolution of dynamical systems, the stability of equilibrium configuration, wave propagation, diffusion, and control and optimization.
Caption: Figure 1: The stability of equilibrium point in [delta]-M plane.
The global stability of equilibrium [U.sup.(2).sub.1] is given in the following theorem.
To guarantee local stability of equilibrium, it is necessary to ensure that all eigenvalues of system (1) in its Jacobian matrix evaluated in the MFE have negative values.
In Section 3, the existence and local stability of equilibrium points are discussed.
For example, in 2015, Zhou utilized Brouwer's fixed point theorem to prove the existence and uniqueness of equilibrium of the hybrid BAM neural networks with proportional delays and finally constructed appropriate delay differential inequalities to derive the stability of equilibrium [28].
(6) Samuelson (1947: 22) adds that economics is not only about maximizing profits of firms or the utility of consumers, it is also concerned about the stability of equilibrium. This issue is picked up in Section III.
In the present study cobweb model was used to know the status of stability of equilibrium on the line of work done by Xu Lingling (2012), Ezekiel M.
Stability of equilibrium then requires that the IS schedule slopes upwards less steeply than the LM schedule.
It is clear that the stability of equilibrium of system (12) is equivalent to the stability of zero solution of system (14).
The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion.