On the Euler Equation: Bi-Hamiltonian Structure and Integrals in Involution

Letters in Mathematical Physics

Volumn 37, Issue 2, 1996, Pages 117-135

  Morosi, Carlo ^a   Pizzocchero, Livio ^b,c  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

^c INFN SEZIONE DI MILANO   (Italy)

Author keywords

Euler equations on Lie algebras; Hamiltonian structures; Integrable systems

Indexed keywords

EID: 0001655833     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00416015     Document Type: Article

References (12)

1. Arnol'd, V. I.: Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier 16 (1966), 319-361.
2. Adler, M., van Moerbeke, P.: Completely integrable systems, Kac-Moody Lie algebras and curves, Adv. in Math. 38 (1980), 267-317.
3. Dikii, L. A.: Hamiltonian systems connected with the rotation group, Funct. Anal. Appl. 6 (1972), 326-327.
4. Libermann, P. and Marle, C. M.: Symplectic Geometry and Analytical Mechanics, D. Reidel, Dordrecht, 1987.
5. Magri, F.: A simple model of the integrable Hamiltonian equation, J. Math. Phys. 19 (1978), 1156-1162.
6. Manakov, S. V.: Note on the integration of Euler's equations of the dynamics of an n-dimensional rigid body, Funct. Anal. Appl. 10 (1976), 328-329.
7. Meshcheryakov, M. V.: A characteristic property of the inertia tensor of a multi-dimensional rigid body, Russian Math. Surveys 38 (1983), 156-157.
8. Mishchenko, A. S., Fomenko, A. T.: Euler's equations on finite-dimensional Lie groups, Math. USSR Izv. 12 (1978), 371-389.
9. Mishchenko, A. S.: Integral geodesics of a flow on Lie groups, Funct. Anal. Appl. 4 (1970), 232-235.
10. Ratiu, T.: The motion of the free n-dimensional rigid body, Indiana Univ. Math. J. 29 (1980), 609-629.
11. Reyman, A. G. and Semenov-Tian-Shansky, M. A.: Group theoretical methods in the theory of finite dimensional integrable systems, in V. I. Arnol'd and S. P. Novikov (eds), Dynamical Systems VII, Springer, Berlin, 1994, pp. 116-225.
12. Ugaglia, M.: Sistemi dinamici integrabili su algebre di Lie: funzioni di Casimir e significato del parametro spettrale, Thesis, Phys. Dept., Univ. of Torino, 1994.