The dynamical behavior of autonomous and continuous elastic systems is studied qualitatively in terms of trajectories in appropriately defined functional phase spaces. It is found that the local stability of equilibrium configurations in a dynamical sense and the stability in the large may be investigated in a more satisfactory manner by adopting this approach. By studying the distribution of the equilibrium configurations in the functional phase space and by extending Liapunov's theorems on stability to continuous systems, sufficiency regions of stability can be established for the following types of problems;elastic systems subjected to (at t=O) impulsive body loads, sudden changes of body loads, sudden changes of boundary conditions of "traction" type, and sudden changes of body loads of finite duration.
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