Meccanica

, Volume 4, Issue 1, pp 3–11 | Cite as

Dissipativity and Lie-admissible algebras

  • Ruggero M. Santilli
Article

Summary

The validity of Hamiltonian mechanics and Lie algebra invariance for free fields and their difficulties for interacting fields are recalled. The role of dissipativity is discussed as an approach allowing the introduction for interacting regions of larger analytical dynamics and algebraic formulations related by the enlarged bracket. A working criterion is introduced in terms of Lie-admissible algebras and the pseudo-Hamiltonian mechanics introduced by R. J. Duffin for discrete dissipative systems is considered as an explicit choice able to reduce to the Hamiltonian mechanics when the systems become conservative. An example of dissipative plasma is explicitly investigated. Furthermore the procedure is extended to continuous systems and classical interpolating dissipative fields induced by Lie-admissible structures are constructed.

Keywords

Mechanical Engineer Civil Engineer Alla Analytical Dynamic Continuous System 

Sommario

Si richiama la validità della Meccanica Hamiltoniana e l'invarianza secondo le algebre di Lie per campi liberi, insieme alle loro difficoltà per campi interagenti. Si discute il ruolo della dissipatività dei campi interpolati come un indirizzo che permette l'introduzione per le regioni di interazione di più larghe strutture analitiche ed algebriche connesse da parentesi di Poisson generalizzate. Si introduce un criterio di lavoro espresso in termini di algebre Lie-ammissibili, il quale da luogo alla Meccanica Pseudo-Hamiltoniana introdotta da R. J. Duffin nel 1962 per sistemi classici, discreti e dissipativi. Come esempio di applicazione fisica si costruisce un modello di plasma dissipativo e si mostra come i parametri della formulazione influenzano il vettore corrente elettrica ed il tensore di conduttività. Inoltre la procedura viene estesa a sistemi classici, continui e dissipativi costruendo, come applicazione, alcuni esempi di equazioni differenziali per campi interpolati indotte da strutture di tipo Lieammissibile.

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References

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Copyright information

© Tamburini Editore s.p.a. Milano 1966

Authors and Affiliations

  • Ruggero M. Santilli
    • 1
  1. 1.Physics DepartmentBoston UniversityBostonUSA

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