Invariants and labels for Lie-Poisson Systems

Technical Report · Wed Apr 01 04:00:00 EST 1998

DOI:https://doi.org/10.2172/594419· OSTI ID:594419

Thiffeault, J L; Morrison, P J

Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system.

• Research Organization: Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: FG03-96ER54346
• OSTI ID: 594419
• Report Number(s): DOE/ER/54346--815; IFSR--815; ON: DE98004876
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
CASIMIR OPERATORS
HAMILTONIANS
INVARIANCE PRINCIPLES
LIE GROUPS
MAGNETOHYDRODYNAMICS