A didactic plot to understand and to present the Cauchy's argument principle (complex Mapping Theorem) and the Nyquist Stability Criterion.
The are four preprogrammed contours given by the variable "op".
'ret'; pts = [x0,y0, x1,y1]; % The vertices of a rectangle
'circle'; pts = [R, xc,yc]; % The radius and center of a circle
'ny_base'; pts = [R, xc,yc]; % The radius of a right semicircle and its center
'ny_desv'; pts = [R, xc,yc, epsilon]; % 'nybase' with a semicircle detour of radius epsilon.
Each preprogrammed contour is presented in four different colors and linestyles, enabling a fast understanding of the direction of the contour and the relationship between the contour in the s-plane and transformed one in the F(s)-plane.
Two possible animations:
1 - Both paths are drawn at the same time.
2 - After plotting the contour and the transformed contour, it is possible to run an animation of a point moving around both paths.
Minor erros on axis during animations corrected.
Change from a step-size-based path construction to a number-of-elements based construction.