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Hence, a stable periodic orbit bifurcates from the critical equilibrium position after the threshold speed is exceeded.
For large-amplitude chatter behaviors, the periodic solutions bifurcated from the critical equilibrium are calculated by the MHB.
Also, it is demonstrated that the critical equilibrium temperatures for phase transformation is important for good agreement between the simulated and experimental hardening depth.
Goodell may believe that his job, as he told Time Magazine in a recent cover story, "is a balancing act". But the past couple of years have showed he's not always so adept at finding the critical equilibrium that leadership requires.
The first is the strength reserving definition, which defines the factor of safety as the factor by which the shear strength of the soil would have to be divided to bring the slope into the state of critical equilibrium.
For a perfectly balanced system, the instability from certain critical equilibrium positions is proved to be the result of Hopf bifurcation and only the supercritical type is found for a specific rotor system using Poore's algebraic criteria.
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Based on the obtained post-critical equilibrium paths, the critical load of the structure was determined by approximation methods.
This leads to a set of non-linear algebraic equations, comprising post-critical equilibrium paths and damage propagation.
In the experiments, post-critical equilibrium paths of the structure were determined, defining the relationship between compressive force and deflection and enabling the validation of the numerical models.
In his book Darwin's Dangerous Idea, philosopher Daniel Dennett is especially critical of Gould's presentation of punctuated equilibrium.
Hence, the factor of safety (FS) was calculated as the soil shear ratio that is necessary to maintain the critical state equilibrium on a potential sliding surface.
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