About peripheral zone of disturbance from the local impulse in string mesh formed by two

I. A. Volkov ; I. A. Kushmar

Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 107-116

Résumé

The base of work is recurrence relations of new type – relations for squares of normalized orthogonal polynomials with application to the problems of transverse oscillations of string mesh. The displacement function of the local impulse for string mech in the form of Kravchuk polynomials has been presented. Discrete variables of Kravchuk polynomials are dual numbers of nodal points and whole-number time, thouse counted from the place and time of application of impulse. With the use of the Szego generalization for Lageere's polynomials the asymptotical performance of influence function wenn strings of two systems differs essentially by ones characteristical impedances has been obtained. Entering of coordinates moving together with the expanding influence front helped for analyses of the displacement epure for the first waves and dynamic of them changes. The linear equation with the first derivatives for squares of normalized orthogonal Lagerr's polynomials in author modification that continualy described wave process in the whole has been derived.