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Quadratic Integrals of Motion and Stellar Orbits in the Absence of Axial Symmetry of the Potential

Published online by Cambridge University Press:  04 August 2017

G.G. Kuzmin
G.G. Kuzmin*
Affiliation:
Tartu Astrophysical Observatory, 202444 Toeravere, Estonia, USSR

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As is well known, in the case of an axially symmetric and time-invariant gravitational potential, if the potential satisfies one particular additional constraint, there exist three isolating integrals of motion: the energy integral, the area integral, and the third integral which is quadratic in the velocities. This work discusses the case in which there exist quadratic integrals in the absence of axial symmetry of the potential. Such a case has already been examined by Eddington [1], but in their explicit form, the integrals were introduced by Clark [2].

References

REFERENCES

1. Eddington, A.S., 1916. Mon. Not. R. astr. Soc., 76, 37.CrossRefGoogle Scholar
2. Clark, G.L., 1936. Mon. Not. R. astr. Soc., 97, 182.Google Scholar
3. Kuzmin, G.G., 1956. Astr. Zh., 33, 27. (Tartu Astr. Obs. Teated, 2).Google Scholar
4. Kuzmin, G.G., 1963. Publ. Tartu Astroph. Obs., 34, 18.Google Scholar