Nonlinear Dynamics in Engineering Systems pp 91-98 | Cite as
Analysis of Dynamical Systems by Truncated Point Mappings and Cell Mapping
Summary
Recent results obtained by the authors on the utility of truncated point mappings applicable to the analysis of multidimensional, multiparameter, periodic nonlinear systems are presented here. Based on multinomial truncation, an explicit analytical expression is determined for the point mapping in terms of the states and parameters of the system to any order of approximation. By combining this approach with analytical techniques, such as the perturbation method employed here, we obtain a powerful tool for finding periodic solutions and for analyzing their stability. A new approach for analyzing nonlinear systems which combines the techniques of truncated point mapping and cell mapping methods is also described here.
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