Abstract
A method is proposed within the framework of linear and regular celestial mechanics /1/, which at the expense of introducing regularizing variables permits the removal of a pole-type singularity existing in the presence of a central body and which also reduces the equations of motion to linear form by giving them the form of the equations of motion of a harmonic oscillator. This connection with the theory of oscillations of a harmonic oscillator permits an analysis from a single viewpoint of various types of motions because the energy constant h occurs as a parameter in the equation itself. A relation determining the regularizing function under a specified field potential is obtained. Using regularization the solutions can be represented in a uniformized form, which avoids the necessity of examining the branching of the solutions, arising when going around the critical points. Uniformization in the large /2/ is achieved by using elliptic functions. The perturbed Kepler motion is considered as an application of the uniformization method.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
