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The stable, left half s-plane maps into the interior of the unit circle of the z-plane, with the s-plane origin equating to |z| = 1 (because e 0 = 1). A diagonal line of constant damping in the s-plane maps around a spiral from (1,0) in the z plane as it curves in toward the origin.
The s-plane poles and zeros of a 5th-order Chebyshev type II lowpass filter to be approximated as a discrete-time filter The z-plane poles and zeros of the discrete-time Chebyshev filter, as mapped into the z-plane using the matched Z-transform method with T = 1/10 second.
Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...
With enough of these arrows in place the system behaviour over the regions of plane in analysis can be visualized and limit cycles can be easily identified. The entire field is the phase portrait, a particular path taken along a flow line (i.e. a path always tangent to the vectors) is a phase path. The flows in the vector field indicate the ...
An isocline (a series of lines with the same slope) is often used to supplement the slope field. In an equation of the form y ′ = f ( x , y ) {\displaystyle y'=f(x,y)} , the isocline is a line in the x , y {\displaystyle x,y} -plane obtained by setting f ( x , y ) {\displaystyle f(x,y)} equal to a constant.
The green lines represent the Sun-Earth-Probe angle upon departure. [clarification needed] In orbital mechanics, a porkchop plot (also pork-chop plot) is a chart that shows level curves of equal characteristic energy (C 3) against combinations of launch date and arrival date for a particular interplanetary flight. [1]
In these figures, the red curves are the lines of curvature for one family of principal directions, and the blue curves for the other. When a line of curvature has a local extremum of the same principal curvature then the curve has a ridge point. These ridge points form curves on the surface called ridges. The ridge curves pass through the ...
Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...