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In this study, the analytical elucidation for a generalized rotational harmonic system that possesses coherence and periodically excited force is reported. The methods of multiple scales within the interferometry are applied to evaluate the proposed problem and certain distinguishable cases for the rotational oscillators including normal harmonic oscillators without damped rotating are explored and discussed in detail. The distinctive computations for all mentioned chaotic cases about source peculiarities are deduced in detail. The acquired results are demonstrated in concrete graphical and numerical examples. Also, the coherence and the corresponding chaotic characteristics are discussed to probe the system intrinsic configurations. We can differentiate between correlations that result from particular multi-particle formation dynamics and even those caused by the influences of quantum symmetrization. We specifically demonstrate periodic flows and the interferences within the symmetrization for the partially chaotic systems obtained with the smashing of particles that is significant compared to the particle mass m. The partially chaotic system exhibits the coherence components which suppress the correlation intercept significantly and thus the current technique measures the degree of coherence precisely. The contemplated methodology can be applied to evaluating and analyzing many strong nonlinear oscillatory equations. Such an innovative approach can compute the problems of celestial mechanics and chemical reactions in engineering and medical fields.
Bary et al. (Thu,) studied this question.