Stability of Critical Equilibrium States

Examines the stability of equilibrium states in nonlinear ordinary differential equations, specifically in cases where a linear approximation is insufficient to determine whether the equilibrium is stable or not. Beginning with a basic introduction, it will be useful to researchers, scientists & engineers working in applications without a background in nonlinear analysis. The latter part is directed at mathematicians & specialists in mechanics interested in the general theory of stability of motion & the problems of nonlinear analysis. Features an extensive discussion of all twenty of the critical & near- critical cases for systems of low co-dimensions & an examination of the stability of equilibrium states of Hamiltonian systems.