Abstract
The matrizants of simply and doubly symmetric orbits of the three-dimensional restricted problem of three bodies because of their symplectic character, can be transformed by means of multiplication with constant matrices into symmetric ones. As a result the bilinear relations between their elements, existing on account of the symplectic property, take linear and very simple forms. This fact is very useful in computer applications where these relations are used as criteria of accuracy.
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References
Bray, T. A. and Goudas, C. L.: 1967, ‘Three-Dimensional Periodic Oscillations’ inAdvances in Astronomy and Astrophysics, Vol. 5, Academic Press New York.
Bray, T. A., and Goudas, C. L.: 1967a,Astron. J. 72, 202–213.
G. Katsiaris: 1969, ‘Simply Symmetric Periodic, Orbits in the Restricted Problem of Three Bodies’, Doctoral Dissertation, Technical University of Athens, Greece.
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Katsiaris, G., Goudas, C.L. The symplectic property of matrizants. Astrophys Space Sci 8, 243–250 (1970). https://doi.org/10.1007/BF00650886
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DOI: https://doi.org/10.1007/BF00650886