Contact Transformation


Also found in: Wikipedia.

contact transformation

[′kän‚takt ‚tranz·fər′mā·shən]
(mathematics)

Contact Transformation

 

a transformation of plane curves such that two mutually tangent curves are transformed into two other curves that are also tangent to each other. A contact transformation is defined by the formulas

(*) X = f (x, y, yʹ) Y = ɸ(x, y, yʹ)

where x and y are the coordinates of the variable point of a curve and X and Y are the coordinates of the variable points of the curve’s image. In order that the formula (*) define a contact transformation, = dY/dX must be independent of y” = d2y/dx2. Examples of contact transformations are point transformations, which are defined by the formulas

X = f (x, y) Y = ɸ(x, y)

and the Legendre transformations.

Contact transformations are used in the theory of differential equations and in differential geometry. The general theory of contact transformations was developed by M. S. Lie. Contact transformations of surfaces in space are defined in an analogous fashion.

REFERENCES

Goursat, E. Kurs matematicheskogo analiza, 3rd ed., vol. 1. Moscow-Leningrad, 1936. (Translated from French.)
Rashevskii, P. K. Geometricheskaia teoriia uravnenii s chastnymi proizvodnymi. Moscow-Leningrad, 1947. [20–1721—2]
References in periodicals archive ?
lt;p>The Oracle-Cisco Customer Contact Transformation Solution promises to bring together customer relationship management, analytics, workflow performance, and hiring software applications with collaboration products.
West Interactive, a leading provider of customer contact transformation solutions, today announced that its Holly Voice Platform received a "Positive" rating in Gartner's 2012 MarketScope for IVR Systems and Enterprise Voice Portals, released Aug.
We consider this rating to reflect our strong ability to deliver market-leading products, our positive client feedback, and our vision of the future regarding IVR and customer contact transformation.
High-performing companies recognize that customer satisfaction is built or destroyed by how well they coordinate every step of each interaction - they're focused on translating their existing service technology investments into satisfying experiences that keep customers coming back," said Robert Wollan, Accenture managing partner, Customer Contact Transformation.
Customers really want their service experience to be more like a good short cut - they expect the first customer service representative they talk with to have the knowledge, tools and capabilities required to address their needs," said Robert Wollan, managing partner of Accenture's Customer Contact Transformation business .