Astronomical School’s Report, 2003, Volume 4, Issue 1, Pages 14–24

https://doi.org/10.18372/2411-6602.04.1014
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UDC 542

Modification of the error ellipsoid under mass point motion

Antonov V.A.

Pulkovo Observatory, Russia

Abstract

The motion of a mass point in an arbitrary force field is studied by means of the deformation of the phase space. Points which represent the variety of initial conditions fill a small ellipsoid in the phase space. One can select such combinations of ellipsoid parameters which remain invariant during the motion, independent of the particular kind of the force field. The number of such invariants is always equal to the number of degrees of freedom. One of the invariants can coincide with the size of the phase volume (Liouville’s theorem).

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References

  1. Appel’ P. Teoreticheskaya mekhanika. Vol. 2 – M.: Fizmatgiz, 1960.
  2. Duboshin G.N. Nebesnaya mekhanika. Osnovnye zadachi i metody, M.: Fizmatgiz, 1963.
  3. Born M., Uspekhi fiz. nauk, 1959, 69, P. 173.

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