Application of generalized Helmholtz conditions to nonlinear stabilization function

Baumgarte's stabilization method is applied to achieve stability in inverse dynamical problem. Helmholtz conditions are considered to check whether an obtained system will be reducible to the form of Lagrange equations of the second kind with Rayleigh dissipation function. Some conditions can be considered as differential equations with respect to stabilization function. In this paper we investigate all their possible solutions and their properties.