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The damping ratio is a system parameter, denoted by ζ ("zeta"), that can vary from undamped (ζ = 0), underdamped (ζ < 1) through critically damped (ζ = 1) to overdamped (ζ > 1). The behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering , chemical engineering , mechanical ...
In mathematics, the Ruelle zeta function is a zeta function associated with a dynamical system. It is named after mathematical physicist David Ruelle . Formal definition
The settling time for a second order, underdamped system responding to a step response can be approximated if the damping ratio by = () A general form is T s = − ln ( tolerance fraction × 1 − ζ 2 ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln({\text{tolerance fraction}}\times {\sqrt {1-\zeta ^{2}}})}{{\text ...
In control theory, overshoot refers to an output exceeding its final, steady-state value. [2] For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step
Riemann zeta function, the archetypal example; Ruelle zeta function; Selberg zeta function of a Riemann surface; Shimizu L-function; Shintani zeta function; Subgroup zeta function; Witten zeta function of a Lie group; Zeta function of an incidence algebra, a function that maps every interval of a poset to the constant value 1. Despite not ...
The root locus of a feedback system is the graphical representation in the complex s-plane of the possible locations of its closed-loop poles for varying values of a certain system parameter. The points that are part of the root locus satisfy the angle condition.
For example, metric dimension is defined in terms of the resolving set for a graph. Dimension has also been defined based on the box covering method applied to graphs. [1] Here we describe the definition based on the complex network zeta function. [2] This generalises the definition based on the scaling property of the volume with distance. [3]
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.