ABSTRACT

The most general mathematical description of the class of systems under consideration is given by systems of ordinary differential equations in the normal Cauchy form. According to general principles, the presence of various parameters changing the properties of the initial system can be mathematically described by introducing free variables (parameters) into equations of its mathematical model. Therefore, we can write a parametric model of a finite-dimensional continuous system in an expanded form. Sensitivity equations with respect to parameter α are linear with respect to corresponding sensitivity functions. The chapter discusses the problem of expanding of parametric families of solutions into power series in parameters values. Using sensitivity equations, it is possible, generally speaking, to obtain some estimates of the error of representation of additional motion in the form of a power series in parameter value. The chapter demonstrates the possibility of applying Lyapunov’s principle for evaluation of the norm of additional motion.