American Institute of Mathematical Sciences

Advanced
February  2005, 5(1): 35-50. doi: 10.3934/dcdsb.2005.5.35

Dynamics of a circular cylinder interacting with point vortices

A. V. Borisov 1, , I. S. Mamaev 1, and  S. M. Ramodanov 2,

1. 

Institute of Computer Science, 1, Universitetskaya str., 426034, Izhevsk, Russian Federation, Russian Federation
2. 

Department of Theoretical Mechanics, Moscow State University, Vorobyevy Gory, 119899, Moscow, Russian Federation

Received  September 2003 Revised  December 2003 Published  November 2004

The paper studies the system of a rigid body interacting dynamically with point vortices in a perfect fluid. For arbitrary value of vortex strengths and circulation around the cylinder the system is shown to be Hamiltonian (the corresponding Poisson bracket structure is rather complicated). We also reduced the number of degrees of freedom of the system by two using the reduction by symmetry technique and performed a thorough qualitative analysis of the integrable system of a cylinder interacting with one vortex.
Keywords: Point vortex, integrable system, Hamiltonian system, qualitative and topological analysis., Poisson bracket structure, first integral, advection.
Mathematics Subject Classification: 37N10, 76B4.
Citation: A. V. Borisov, I. S. Mamaev, S. M. Ramodanov. Dynamics of a circular cylinder interacting with point vortices. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 35-50. doi: 10.3934/dcdsb.2005.5.35
[1]

Dan Wei, Shangjiang Guo. Qualitative analysis of a Lotka-Volterra competition-diffusion-advection system. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2599-2623. doi: 10.3934/dcdsb.2020197
[2]

Qi Wang, Chunyi Gai, Jingda Yan. Qualitative analysis of a Lotka-Volterra competition system with advection. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1239-1284. doi: 10.3934/dcds.2015.35.1239
[3]

Francisco Crespo, Francisco Javier Molero, Sebastián Ferrer. Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier. Journal of Geometric Mechanics, 2016, 8 (2) : 169-178. doi: 10.3934/jgm.2016002
[4]

Gianluca Crippa, Milton C. Lopes Filho, Evelyne Miot, Helena J. Nussenzveig Lopes. Flows of vector fields with point singularities and the vortex-wave system. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2405-2417. doi: 10.3934/dcds.2016.36.2405
[5]

Lu Chen, Zhao Liu, Guozhen Lu. Qualitative properties of solutions to an integral system associated with the Bessel potential. Communications on Pure and Applied Analysis, 2016, 15 (3) : 893-906. doi: 10.3934/cpaa.2016.15.893
[6]

Yuan Lou, Dongmei Xiao, Peng Zhou. Qualitative analysis for a Lotka-Volterra competition system in advective homogeneous environment. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 953-969. doi: 10.3934/dcds.2016.36.953
[7]

Gianluca Crippa, Silvia Ligabue, Chiara Saffirio. Lagrangian solutions to the Vlasov-Poisson system with a point charge. Kinetic and Related Models, 2018, 11 (6) : 1277-1299. doi: 10.3934/krm.2018050
[8]

Sufang Tang, Jingbo Dou. Quantitative analysis of a system of integral equations with weight on the upper half space. Communications on Pure and Applied Analysis, 2022, 21 (1) : 121-140. doi: 10.3934/cpaa.2021171
[9]

Sobhan Seyfaddini. Spectral killers and Poisson bracket invariants. Journal of Modern Dynamics, 2015, 9: 51-66. doi: 10.3934/jmd.2015.9.51
[10]

Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807
[11]

Martina Conte, Maria Groppi, Giampiero Spiga. Qualitative analysis of kinetic-based models for tumor-immune system interaction. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2393-2414. doi: 10.3934/dcdsb.2018060
[12]

Jianquan Li, Xin Xie, Dian Zhang, Jia Li, Xiaolin Lin. Qualitative analysis of a simple tumor-immune system with time delay of tumor action. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5227-5249. doi: 10.3934/dcdsb.2020341
[13]

Shouming Zhou, Shanshan Zheng. Qualitative analysis for a new generalized 2-component Camassa-Holm system. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4659-4675. doi: 10.3934/dcdss.2021132
[14]

Hai-Liang Li, Hongjun Yu, Mingying Zhong. Spectrum structure and optimal decay rate of the relativistic Vlasov-Poisson-Landau system. Kinetic and Related Models, 2017, 10 (4) : 1089-1125. doi: 10.3934/krm.2017043
[15]

Xavier Perrot, Xavier Carton. Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 971-995. doi: 10.3934/dcdsb.2009.11.971
[16]

Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228
[17]

Frol Zapolsky. Quasi-states and the Poisson bracket on surfaces. Journal of Modern Dynamics, 2007, 1 (3) : 465-475. doi: 10.3934/jmd.2007.1.465
[18]

Karina Samvelyan, Frol Zapolsky. Rigidity of the ${{L}^{p}}$-norm of the Poisson bracket on surfaces. Electronic Research Announcements, 2017, 24: 28-37. doi: 10.3934/era.2017.24.004
[19]

Dezhong Chen, Li Ma. A Liouville type Theorem for an integral system. Communications on Pure and Applied Analysis, 2006, 5 (4) : 855-859. doi: 10.3934/cpaa.2006.5.855
[20]

Changlu Liu, Shuangli Qiao. Symmetry and monotonicity for a system of integral equations. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1925-1932. doi: 10.3934/cpaa.2009.8.1925

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (95)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy