Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Note on $ 120$ degree axial coordinates

Author: W. E. Bleick
Journal: Quart. Appl. Math. 43 (1985), 125-126
MSC: Primary 70B99; Secondary 51N20
DOI: https://doi.org/10.1090/qam/782261
MathSciNet review: 782261
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Abstract: Recently the author introduced [1] a symmetrical system of distance coordinates for studying the planar motion of a three-body system of point masses in its internal degrees of freedom, and applied them to the small vibration problem. Subsequently he applied them [2] to the gravitational three-body problem. The purpose of this note is to give a geometrical identification of the auxiliary angles $ {\theta _{1,}}{\theta _{2,}}$, and $ {\theta _3}$, related to the system, and to prove the identity which they satisfy.

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  • [1] W. E. Bleick, New coordinates for three-body problems, Proceedings of the International Symposium on Quantum Chemistry, Theory of Condensed Matter, and Propagator Methods in the Quantum Theory of Matter (Flagler Beach, Fla., 1982), 1982, pp. 241–245. MR 698245, https://doi.org/10.1002/qua.560220825
  • [2] Bleick, W. E., Gravitational three-body problem in 120 deg axial coordinates, Journal of Guidance, Control and Dynamics, 6 124-128 (1983)

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DOI: https://doi.org/10.1090/qam/782261
Article copyright: © Copyright 1985 American Mathematical Society

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