Grandori Guagenti, Elisa:
Su di un invariante integrale dei continui hamiltoniani
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 56 (1974), fasc. n.1, p. 65-71, (Italian)
pdf, djvu. | Zbl 0305.73008
Sunto
This paper deals with continuous mechanical systems, following hamiltonian formalism. It is shown that each continuous system has invariant integrals of the type of Poincaré's invariant integrals. Two examples are discussed: Thomson theorem in fluid dynamics is found again, then it is extended to magnetofluid dynamics.
Referenze Bibliografiche
[1]
KOLMOGOROV A. N.,
On the conservation of Quasi-Periodic Motions for a Small Change in the Hamiltonian Function, «
Dokl. Akad. Nauk.»,
98, 4 (
1954). |
MR 68687[2]
ARNOLD V. I. e
AVEZ A.,
Ergodic Problems of Classical Mechanics,
Benjamin W. A., Inc.,
1968. |
MR 232910 |
Zbl 0715.70004[4]
TER HAAR D.,
Elements of Hamiltonian Mechanics,
North Holland Publ. Comp., Amsterdam,
1961. |
MR 128100 |
Zbl 0111.19302[5] GOLDSTEIN H., Meccanica classica, Zanichelli, Bologna 1961.
[6] SCHIFF L. I., Quantum Mechanics, McGraw Hill, New York, 1949.
[7] UDESCHINI P., Sulla forma hamiltoniana della teoria einsteiniana della gravitazione, «Rend. Sem. Mat. Fis.», Milano 1968.
[8]
WHITTAKER E. T.,
Analytical Dynamics of Particles and Rigid Bodies,
Dover Publ., New York,
1944. |
MR 10813 |
Zbl 0061.41806[9] GANTMACHER F., Lectures in Analytical Mechanics, MIR Publ., Moscow, 1970.
[10]
CARTAN E.,
Leçons sur les invariants intégraux,
Hermann, Paris,
1971. |
MR 355764[11]
MATTEI G.,
The Lagrangian and Hamiltonian Formulation for Magneto-Fluid-Dynamics Waves, «
Boll. U.M.I.»,
4, 7 (
1973). |
Zbl 0268.76079