A model which allows a double impacting regime for a particle undergoing simple harmonic motion is considered in some detail. The behavior of the particle in the weak spring limit is considered. Symmetries of the motion are found and the extent of the resonant dynamical behavior is considered. Control equations are developed and strategies are described for both the preservation and the annihilation of experimental and analytical resonant periodic orbits.
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Gutiérrez et al. (2004) studied this question.
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