Abstract
We develop the Hamilton-Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler-Poincaré equations with advective parameters. Then, we derive the reduced Hamilton-Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton-Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler-Poincaré equations.
| Original language | English |
|---|---|
| Title of host publication | AIP Conference Proceedings |
| Pages | 645-647 |
| Number of pages | 3 |
| Volume | 1376 |
| DOIs | |
| Publication status | Published - 2011 |
| Event | Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI - Guangzhou Duration: 2011 Jun 30 → 2011 Jul 3 |
Other
| Other | Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI |
|---|---|
| City | Guangzhou |
| Period | 11/6/30 → 11/7/3 |
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Keywords
- Advective Parameters
- Hamilton-Pontryagin Principle
- Implicit Euler-Poincaré Equations
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Hamilton-Pontryagin principle for incompressible ideal fluids. / Yoshimura, Hiroaki; Gay-Balmaz, François.
AIP Conference Proceedings. Vol. 1376 2011. p. 645-647.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Hamilton-Pontryagin principle for incompressible ideal fluids
AU - Yoshimura, Hiroaki
AU - Gay-Balmaz, François
PY - 2011
Y1 - 2011
N2 - We develop the Hamilton-Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler-Poincaré equations with advective parameters. Then, we derive the reduced Hamilton-Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton-Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler-Poincaré equations.
AB - We develop the Hamilton-Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler-Poincaré equations with advective parameters. Then, we derive the reduced Hamilton-Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton-Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler-Poincaré equations.
KW - Advective Parameters
KW - Hamilton-Pontryagin Principle
KW - Implicit Euler-Poincaré Equations
UR - http://www.scopus.com/inward/record.url?scp=80355144951&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80355144951&partnerID=8YFLogxK
U2 - 10.1063/1.3652002
DO - 10.1063/1.3652002
M3 - Conference contribution
AN - SCOPUS:80355144951
SN - 9780735409361
VL - 1376
SP - 645
EP - 647
BT - AIP Conference Proceedings
ER -