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http://hdl.handle.net/20.500.12188/7171
Наслов: | “Conditions on Nonlinearity of Oscillatory Equations Inducing the Periapsidal Precession”, 51:67 https://doi.org/10.1007/s10714-019-2550-1. 2019 (https://www.springer.com/journal/10714) | Authors: | Celakoska E., Lazarevska A M. | Keywords: | Perturbation methods, Linearization, Perihelion shift, Lambert W function | Issue Date: | 2019 | Publisher: | © Springer Science+Business Media, LLC, part of Springer Nature 2019 (IF 1.515) | Source: | Celakoska, E., Lazarevska, A.M. Conditions on nonlinearity of oscillatory equations inducing the periapsidal precession. Gen Relativ Gravit 51, 67 (2019). https://doi.org/10.1007/s10714-019-2550-1 | Journal: | General Relativity and Gravitation volume 51 | Series/Report no.: | General Relativity and Gravitation;Article number: 67 (2019) | Abstract: | The equations of motion in the theory of general relativity obtained for the Schwarzschild metric yield an oscillatory differential equation with weak quadratic nonlinearity. This nonlinearity induces the well-known parametric expression for the relocation of the orbital periapsis, usually termed as periapsidal precession. It still represents a hard test for a gravitational theory viability. In the standard process of obtaining the precession, some approximation methods are employed, however it seems that the methods can provide better information then it is usually presented in the literature. We give an in-depth analysis of the oscillatory nonlinear differential equation as a dynamical system, also analyzing the conditions for obtaining the precession given other nonlinearities. Then, we outline a procedure for obtaining this precession for more general types of nonlinearities and the conditions which apply on them. | URI: | http://hdl.handle.net/20.500.12188/7171 | DOI: | https://doi.org/10.1007/s10714-019-2550-1 |
Appears in Collections: | Faculty of Mechanical Engineering: Journal Articles |
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