Construction of dynamically equivalent time-invariant forms for time-periodic systems
The authors propose and develop several new general methods for constructing dynamically equivalent time-invariant forms for linear and nonlinear systems with periodic coefficients. The basis of these methods consists in the application of Lyapunov-Floquet transformation and simplification techniques such as center manifold reduction and time-dependent normal form theory. More specifically, in the first section it is shown that a set of linear second-order equations with periodic coefficients can be transformed to an equivalent set of time-invariant second-order equations by an application of a sequence of transformations. It is also shown that a time-periodic quadratic Hamiltonian can be transformed to a time-invariant Hamiltonian by extending this idea. In the second part the authors study time-invariant forms of nonlinear equations. Single and double inverted pendulums subjected to periodic parametric excitation are considered as physical examples of the presented techniques, and the obtained results are verified by numerical simulations.
scientific article; zbMATH DE number 1203544