Extended Graphical Representation of Polynomials with Applications to Cybernetics

作     者：汪家訸 

作者机构：Chekiang University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学(英文版))

年 卷 期：1981年第2卷第3期

页      面：305-318页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：root Extended Graphical Representation of Polynomials with Applications to Cybernetics 

摘      要：In this paper,the polynomial of a complex variable s(≡x+iy)with realcoefficients K=as~n+as+……+as+*** graphically represented by three plane curves which are the projections of aspace curve on three coordinate planes of the coordinate system(x,iy.K)inwhich K is confined to be *** projection on(x,iy)plane is just the rootlocus of the polynomial with K as a real *** is remarkable thatthe equation of the root-locus is m-th degree in y~2,whether n=2m+1 orn=2m+*** addition to the real curve K.=f(x)in the figure(K,x)thereexists another curve *** is plotted by the real parts of all complexroots against ***(K,x)curve is particularly important to determine theabsolute as well as the relative stable interval of K for linear *** cybernetics,the(K,iy)curve can be used to show the relation betweenthe nature frequency ω and the gain *** three figures are useful forstudying the theory of equation and cybernetics.