Patent ID: 6567758
Filing Date: 2003-05-20
Classification: G01H,G06K

Abstract:
A method for analyzing and simulating period phenomena, such as mechanical vibrations and variations in temperature, pressure, fluid flows, electric currents or electric tensions, comprising the steps:generating an integral transform (2) by replacing the Laplace variable s in the conventionally used Laplace transform (0): f&af;(s)=&Integral;tatl&it;&ee;-st&it;y&af;(t)&it;&dd;t(0)with the complex number s+i&sgr;, giving: f&af;(s,Ïƒ)+&ii;&it;â€ƒ&it;&varphi;&af;(s,Ïƒ)=&Integral;tait&it;&ee;-(s+&ii;&it;â€ƒ&it;Ïƒ)&it;t&it;y&af;(t)&it;â€ƒ&it;&dd;t(2)dividing the transform (2) into real and imaginary components,reducing the imaginary component by i giving two integral transforms (3) and (4): f=&Integral;tatl&it;&ee;-st&it;y&af;(t)&it;cos&it;â€ƒ&it;(Ïƒ&it;â€ƒ&it;t)&it;â€ƒ&it;&dd;t(3)and &varphi;=-&Integral;tatl&it;&ee;-st&it;y&af;(t)&it;sin&it;â€ƒ&it;(Ïƒ&it;â€ƒ&it;t)&it;â€ƒ&it;&dd;t(4)in which f and &phgr; are transformation functions, t is the argument of the transformable function, y is a transformable function, s and &sgr; are free variables, and ta and tl are the times of the start and end of the integral transformation, andresolving properties characterizing response curves using the transforms.