Utilization of Symmetry in Non-Linear Equations of the Inverse Vibrational Problem

Abstract

A new general technique is developed for solving the non-linear equations obtained from the secular equation in the inverse vibrational problem. The off-diagonal force constant elements are determined first and the resulting non-linear equations of various degrees in the secular equation are solved by Newton-Raphson's iterative method. This involves the computation of values of the functions and their derivatives for which the new technique exploiting the symmetry in the equations is utilised. The iterative method involves mainly the calculation of the values of the functions and their derivatives at the corresponding points. Here a new general procedure is developed to obtained these values of functions and derivatives using the symmetry in the secular equation.