Dispersion of ensembles of non-interacting particles

Details Dispersion of ensembles of non-interacting particles Dispersion of ensembles of non-interacting particles

Aug 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..43...63h&link_type=abstract

Astrophysics and Space Science, vol. 43, Aug. 1976, p. 63-82.

Physics

Condensed Matter

Statistical Mechanics

2

Astronomical Models, Distribution Functions, Particle Interactions, Particle Motion, Spatial Distribution, Statistical Mechanics, Asteroids, Circular Orbits, Dynamic Models, Linear Systems, Particle Trajectories, Stellar Models, Transcendental Functions

Scientific paper

The dynamics of an ensemble of noninteracting particles dispersing from a common origin and moving in a common force field with an initial distribution of momenta is analyzed using an approach where the particles are considered as a continuum described by a phase-space distribution function. General solutions are obtained for both the distribution function and the associated spatial density function. The linear case of small departures from circular orbits in an axisymmetric gravitational field is treated along with the specific case of particle dispersion from an object in a circular orbit in the same type of field. Numerical results are presented for the latter case, and consideration is given to the inverse problem of determining the initial time and velocity distribution from knowledge of the ensemble structure at a later time. Explicit results are provided for the case of an ellipsoidal distribution of initial momenta, and a numerical procedure is indicated for treating more general cases.

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