Hydrodynamic limits from the self-organized kinetic system for body attitude coordination
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917968092332032 |
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| author | Guo, Naping Luo, Yi-Long |
| author_facet | Guo, Naping Luo, Yi-Long |
| contents | 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 describe a new collective motion for multi-agents dynamics, where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate round it adopting different configurations (representing by rotation matrix in $\mathrm{SO(3)}$). In this paper, we study the hydrodynamic limit of the scaled SOKB system with the 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 transfer SOHB system into a non-singular form by stereographic projection. This work provides the first analytically rigorous justification of the modeling and asymptotic analysis in Degond et al. (Math. Models Methods Appl. Sci. 27(6), 1005-1049, 2017). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_08657 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limits from the self-organized kinetic system for body attitude coordination Guo, Naping Luo, Yi-Long Analysis of PDEs 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 describe a new collective motion for multi-agents dynamics, where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate round it adopting different configurations (representing by rotation matrix in $\mathrm{SO(3)}$). In this paper, we study the hydrodynamic limit of the scaled SOKB system with the 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 transfer SOHB system into a non-singular form by stereographic projection. This work provides the first analytically rigorous justification of the modeling and asymptotic analysis in Degond et al. (Math. Models Methods Appl. Sci. 27(6), 1005-1049, 2017). |
| title | Hydrodynamic limits from the self-organized kinetic system for body attitude coordination |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.08657 |