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We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensembleconfined in a harmonic potential field. In the absence of external force field,emergent dynamics of TCS particles has been extensively studied recently undervarious frameworks formulated in terms of initial configuration, systemparameters and network topologies. Moreover, the TCS model does not exhibitrotating motions in the absence of an external force field. In this paper, weshow the emergence of periodically rotating one-point cluster for the TCS modelin a harmonic potential field using elementary energy estimates and continuityargument. We also provide several numerical simulations and compare them withanalytical results.

Emergence of a periodically rotating one-point cluster in a thermodynamic Cucker-Smale ensemble