TY - JOUR UR - http://lib.ugent.be/catalog/pug01:1231271 ID - pug01:1231271 LA - eng TI - The dynamics of a rigid body in potential flow with circulation PY - 2010 JO - (2010) REGULAR & CHAOTIC DYNAMICS SN - 1560-3547 PB - 2010 AU - Vankerschaver, Joris WE01 001999061882 AU - Kanso, E AU - Marsden, JE AB - We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1231271 | ||
005 | 20180813140749.0 | ||
008 | 110524s2010------------------------eng-- | ||
022 | a 1560-3547 | ||
024 | a 000286401200014 2 wos | ||
024 | a 1854/LU-1231271 2 handle | ||
024 | a 10.1134/S1560354710040143 2 doi | ||
040 | a UGent | ||
245 | a The dynamics of a rigid body in potential flow with circulation | ||
260 | c 2010 | ||
520 | a We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor. | ||
598 | a A1 | ||
100 | a Vankerschaver, Joris u WE01 0 001999061882 0 801001781625 | ||
700 | a Kanso, E | ||
700 | a Marsden, JE | ||
650 | a Mathematics and Statistics | ||
653 | a POINT VORTICES | ||
653 | a POISSON BRACKETS | ||
653 | a STABILITY | ||
653 | a BODIES | ||
653 | a FLUIDS | ||
653 | a SYSTEM | ||
653 | a LIE | ||
653 | a fluid-structure interactions | ||
653 | a potential flow | ||
653 | a circulation | ||
653 | a symplectic reduction | ||
653 | a diffeomorphism groups | ||
653 | a oscillator group | ||
773 | t REGULAR & CHAOTIC DYNAMICS g Regul. Chaotic Dyn. 2010. 15 (4-5) p.606-629 q 15:4-5<606 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1231271/file/1231287 z [open] y VaKaMa2009b-circulation.pdf | ||
920 | a article | ||
852 | x WE b WE01 | ||
922 | a UGENT-WE |
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