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The Bode plotter is an electronic instrument resembling an oscilloscope, which produces a Bode diagram, or a graph, of a circuit's voltage gain or phase shift plotted against frequency in a feedback control system or a filter. An example of this is shown in Figure 10.
The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.
While a system of 3 bodies interacting gravitationally is chaotic, a system of 3 bodies interacting elastically is not. [clarification needed] There is no general closed-form solution to the three-body problem. [1] In other words, it does not have a general solution that can be expressed in terms of a finite number of standard mathematical ...
This page was last edited on 19 July 2005, at 14:41 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let L be the loop transfer function and S be the sensitivity function. In the diagram, P is a dynamical process that has a transfer function P(s).
A continuous-time non-autonomous dynamical system can be defined as, ˙ = (()) + / (()) (()), where is a point in the phase space which can be assumed to be a closed smooth manifold, () is a sufficiently smooth flow vector field from the tangent space of , and , =, …,, = is a set of sufficiently smooth vector fields that specify how the ...
The term, also called the Duffing term, can be approximated as small and the system treated as a perturbed simple harmonic oscillator. The Frobenius method yields a complex but workable solution. Any of the various numeric methods such as Euler's method and Runge–Kutta methods can be used.
The advantage of this technique is that it results in a simplification of the mathematics; the differential equations that represent the system are replaced by algebraic equations in the frequency domain which is much simpler to solve. However, frequency domain techniques can only be used with linear systems, as mentioned above.