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] Bleick, W. E., New coordinates for three-body problems, International Journal of Quantum Chemistry, Vol. 22, Quantum Chemistry Symposium No. 16, 241-245, 1982. MR 698245
  • [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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