The stability of second-order quadratic differential equations

This paper investigates the stability properties of second-order systems.
\dot{x} = f(x)
, where
f(x)
contains either quadratic terms-system (1)-or linear and quadratic terms-system (2)-in
x
. The principal contributions are summarized in two theorems which give necessary, and sufficient conditions for stability and asymptotic stability in the large of systems (1) and (2), respectively.