Abstract
Let us return to the equations of dynamics by assuming only two degrees of freedom and consequently four variables \( x_{1} \), \( x_{2} \), \( y_{1} \), and \( y_{2} \).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
If \( x_{1}^{0} \) and \( x_{2}^{0} \) were selected such that the ratio \( n_{1} /n_{2} \) is commensurable, then one could be satisfied with expanding \( x_{1} \) and \( x_{2} \) in powers of \( \mu \) (and not of \( \sqrt \mu \)). One would then arrive at series, which in truth would not be convergent in the geometric meaning of the word, but which like those of Mr. Lindstedt could be useful in some cases.
- 2.
[Translator: See erratum at end.]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Poincaré, H. (2017). Study of the Asymptotic Surfaces. In: The Three-Body Problem and the Equations of Dynamics. Astrophysics and Space Science Library, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-52899-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-52899-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52898-4
Online ISBN: 978-3-319-52899-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)