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Galactic oscillator symmetry
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Rosensteel, George |
| Copyright Year | 1995 |
| Description | Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities. |
| File Size | 371857 |
| Page Count | 8 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19950016556 |
| Archival Resource Key | ark:/13960/t53f9pj4c |
| Language | English |
| Publisher Date | 1995-01-01 |
| Access Restriction | Open |
| Subject Keyword | Thermodynamics And Statistical Physics Potential Energy Velocity Distribution Rotation Ellipsoids Cauchy Problem Harmonic Oscillators Algebra Astronomical Models Angular Velocity Hamiltonian Functions Kinetic Energy Nuclear Physics Symmetry Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
