Poisson brackets for the dynamically interacting system of a 2D rigid cylinder and N point vortices: The case of arbitrary smooth cylinder shapes

Regular and Chaotic Dynamics

Volumn 10, Issue 1, 2005, Pages 1-14

  Shashikanth, B N ^a  

^a NEW MEXICO STATE UNIVERSITY   (United States)

Author keywords

Hamiltonian; Point vortices; Poisson brackets; Reciprocity; Rigid body

Indexed keywords

EID: 33645580385     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2005v010n01ABEH000295     Document Type: Review

References (25)

1. R. H. Abraham, J. E. Marsden. Foundations of Mechanics. Addison-Wesley. 1978 (out of print), updated version from www.perseusbooksgroup.com.
2. M. Adams, T. Ratiu. The three-point vortex problem: commutative and noncommutative integrability. In "Hamiltonian Dynamical System", Cont. Math. 1988. V. 81. P. 245-257.
3. G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press. 1970.
4. A. V. Borisov, I. S. Mamaev, S. M. Ramodanov. Motion of a circular cylinder and n point vortices in a perfect fluid. Reg. & Chaot. Dyn. 2003. V. 8. No4. P. 449-462.
5. A. V. Borisov, I. S. Mamaev. An integrability of the problem on motion of cylinder and vortex in the ideal fluid. Reg. & Chaot. Dyn. 2003. V. 8. No2. P. 163-166.
6. G. F. D. Duff, D. C. Spencer. Harmonic tensors on Riemannian manifolds with boundary. Ann. Math. 1952. V. 56. No1. P. 128-156.
7. S. D. Kelly. The Mechanics and Control of Robotic Locomotion with Applications to Aquatic Vehicles. Ph. D. Thesis. California Institute of Technology. 1998.
8. C. C. Lin. On the motion of vortices in two dimensions - I and II. Proc. Nat. Acad. Sci. 1941. V. 27. P. 570-577.
9. J. E. Marsden, T. J. R. Hughes. Mathematical Foundations of Elasticity. Dover, New York. 1983.
10. J. E. Marsden, T. S. Ratiu. Introduction to Mechanics and Symmetry. Texts in Applied Mathematics. V. 17. Springer-Verlag, Second Edition. 1999.
11. J. E. Marsden, A. Weinstein. Coadjoint orbits, vortices and Clebsch variables for incompressible fluids. Physica D. 1983. V. 7. P. 305-323.
12. L. M. Milne-Thomson. Theoretical Hydrodynamics (fifth edition). Dover, New York. 1996.
13. L. Quartapelle, F. Valz-Gris. Projection conditions on the vorticity in viscous incompressible flows. Int. J. Num. Meth. Fluids. 1981. V. 1. P. 129-144.
14. J. Radford. Symmetry, Reduction and Swimming in a Perfect Fluid. Ph. D. Thesis. California Institute of Technology. 2003.
15. S. M. Ramodanov. Motion of a circular cylinder and a vortex in an ideal fluid. Reg. & Chaot. Dyn. 2001. V. 6. NO1. P. 33-38.
16. S. M. Ramodanov. Motion of a circular cylinder and N point vortices in a perfect fluid. Reg. & Chaot. Dyn. 2002. V. 7. No3. P. 291-298.
17. B. N. Shashikanth, J. E. Marsden, J. W. Burdick, S. D. Kelly. The Hamiltonian structure of a 2-D rigid circular cylinder interacting dynamically with N point vortices. Phys. Fluids. 2002. V. 14. No3. P. 1214-1227.
18. (Erratum: Phys. Fluids, V. 14, No11, 4099)
19. V. A. Vladimirov. Vortical momentum of flows of an incompressible liquid. J. Appl. Mech. Tech. Phys. 1978. V. 18. P. 791-794.
20. (Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No.6, 72-77, (1977))
21. V. A. Vladimirov. Vortical momentum of bounded ideal incompressible fluid flows. J. Appl. Mech. Tech. Phys. 1979. V. 20. P. 157-163.
22. (Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No.2, 53-61, (1979))
23. J. C. Wells. A geometrical interpretation of force on a translating body in rotational flow. Phys. Fluids. 1996. V. 8. No2. P. 442-450.
24. J. C. Wells. Calculating the impulse and angular impulse of image vorticity by integrals over free vorticity. Proc. R. Soc. London Ser. A. 1998. V. 454. P. 2791-2809.
25. H. Weyl. The method of orthogonal projection in potential theory. Ann. Math. 1940. V. 7. P. 411-444.