1. Science
  2. Publications
  3. Information Processing Systems
  4. 12(137)'2015
  5. Applications of differential calculus to geometry of elementary catastrophes. umbilical catastrophes

Applications of differential calculus to geometry of elementary catastrophes. umbilical catastrophes

V.Yu. Dubnitskiy, A.I. Khodyrev
Annotations languages:

For umbilical catastrophes it is proposed to determine elementary differential geometric characteristics of their potential functions, such as curvature, radius of curvature, curvature center coordinates. Those characteristics were obtained in explicit form for potential functions of catastrophes which have elliptical, hyperbolic, parabolic first type and parabolic second type umbilicals.
Keywords: theory of catastrophes, potential functions of catastrophes, umbilicals, elliptic umbilical, hyperbolic umbilical, parabolic first type umbilical, parabolic second type umbilical, curvature, radius of curvature, curvature center coordinates