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  2. Stability theory - Wikipedia

    en.wikipedia.org/wiki/Stability_theory

    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 ...

  3. Equilibrium point (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Equilibrium_point...

    If at least one has a positive real part, the point is unstable. If at least one eigenvalue has negative real part and at least one has positive real part, the equilibrium is a saddle point and it is unstable. If all the eigenvalues are real and have the same sign the point is called a node.

  4. Mechanical equilibrium - Wikipedia

    en.wikipedia.org/wiki/Mechanical_equilibrium

    Diagram of a ball placed in an unstable equilibrium. Second derivative < 0 The potential energy is at a local maximum, which means that the system is in an unstable equilibrium state. If the system is displaced an arbitrarily small distance from the equilibrium state, the forces of the system cause it to move even farther away.

  5. Statically indeterminate - Wikipedia

    en.wikipedia.org/wiki/Statically_indeterminate

    In order to distinguish between this and the situation when a system under equilibrium is perturbed and becomes unstable, it is preferable to use the phrase partly constrained here. In this case, the two unknowns V A and V C can be determined by resolving the vertical force equation and the moment equation simultaneously. The solution yields ...

  6. Economic equilibrium - Wikipedia

    en.wikipedia.org/wiki/Economic_equilibrium

    Even if it satisfies properties P1 and P2, the absence of P3 means that the market can only be in the unstable equilibrium if it starts off there. In most simple microeconomic stories of supply and demand a static equilibrium is observed in a market; however, economic equilibrium can be also dynamic.

  7. Linear stability - Wikipedia

    en.wikipedia.org/wiki/Linear_stability

    In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form / =, where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part.

  8. Angle of loll - Wikipedia

    en.wikipedia.org/wiki/Angle_of_loll

    Angle of loll is the state of a ship that is unstable when upright (i.e. has a negative metacentric height) and therefore takes on an angle of heel to either port or starboard. When a vessel has negative metacentric height (GM) i.e. , is in unstable equilibrium, any external force applied to the vessel will cause it to start heeling.

  9. Steady state - Wikipedia

    en.wikipedia.org/wiki/Steady_state

    An unstable system is one that diverges from the steady state. See for example Linear difference equation#Stability . In chemistry , a steady state is a more general situation than dynamic equilibrium .