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<p>The self-organized kinetic system for body attitude coordination (SOKB) was recently derived by Degond et al. (Math. Models Methods Appl. Sci. 27(6), 1005-1049, 2017). This system describes the collective motion for multi-agent dynamics, where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction, while their bodies can rotate about this direction adopting different configurations represented by rotation matrices in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathrm {SO(3)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">SO</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we study the hydrodynamic limit of the scaled SOKB system with constant intensity of coordination by employing the Generalized Collision Invariants (GCI)-based Hilbert expansion approach. The limit is the self-organized hydrodynamic model for body attitude coordination (SOHB). In spherical coordinates, the SOHB system is singular. To avoid this coordinate singularity, we transform the SOHB system into a non-singular form via stereographic projection. This work provides the first rigorous analytical justification for the formal modeling and asymptotic analysis presented in the aforementioned work.</p>

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Hydrodynamic Limits From the Self-Organized Kinetic System for Body Attitude Coordination

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Naping Guo,
  • Yi-Long Luo

摘要

The self-organized kinetic system for body attitude coordination (SOKB) was recently derived by Degond et al. (Math. Models Methods Appl. Sci. 27(6), 1005-1049, 2017). This system describes the collective motion for multi-agent dynamics, where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction, while their bodies can rotate about this direction adopting different configurations represented by rotation matrices in \(\mathrm {SO(3)}\) SO ( 3 ) . In this paper, we study the hydrodynamic limit of the scaled SOKB system with constant intensity of coordination by employing the Generalized Collision Invariants (GCI)-based Hilbert expansion approach. The limit is the self-organized hydrodynamic model for body attitude coordination (SOHB). In spherical coordinates, the SOHB system is singular. To avoid this coordinate singularity, we transform the SOHB system into a non-singular form via stereographic projection. This work provides the first rigorous analytical justification for the formal modeling and asymptotic analysis presented in the aforementioned work.