Basins of Convergence in a Multi-Perturbed CR3BP
Source abstract
Abstract
The circular restricted three-body problem (CR3BP) is analyzed to introduce additional factors into the dynamic model, such as radiation forces, flattening of the primary bodies, relativity effects, and the presence of natural satellites. The introduction of these factors increases the accuracy when obtaining the position of the Lagrange points and the basins of convergence of the system. The Newton–Raphson methodis used to implement a searching algorithm. Finally, an application to the Sun–Mars system including the presence of Phobos and Deimos is developed.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Vibration and Dynamic Analysis · Advanced Control Systems Optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Instituto de Diseño y Fabricación, Universitat Politècnica de València, 46022 Valencia, Spain
Funding
European Union Next Generation EU/PRTR · Generalitat Valenciana, Spain
References (34)
Show source-provided references
1. NASA. Discovery Program (2021, December 12). InSight (Discovery Mission), Available online: https://mars.nasa.gov/insight/.
2. NASA (2021, December 12). Mars 2020 Mission Perseverance Rover, Available online: https://mars.nasa.gov/mars2020/.
3. China National Space Administration (2021, December 12). Tianwen 1 Mars Mission 2021, Available online: http://www.cnsa.gov.cn/english/n6465652/n6465653/c6809448/content.html.
4. ESA/Roscosmos (2021, December 12). ExoMars 2022 Rover and Surface Platform. Available online: https://exploration.esa.int/web/mars/-/45084-exomars-rover.
5. The Gaia mission10.1051/0004-6361/201629272 ↗
6. An Introduction to the Classical Three-Body Problem10.1007/s12045-019-0760-1 ↗
7. The photogravitational restricted three-body problem
8. Existence and stability of triangular points in the restricted three-body problem with numerical applications10.1007/s10509-012-1162-y ↗
9. Periodic orbits around the collinear libration points10.22436/jnsa.009.04.27 ↗
10. The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits10.3934/dcdss.2019057 ↗
11. The planar re- stricted three-body problem when both primaries are triaxial rigid bodies: Equilibrium points and periodic orbits10.1007/s10509-016-2894-x ↗
12. Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential10.1016/j.chaos.2020.109704 ↗
13. Johnston, H., Lo, M.W., and Mortari, D. (2021). A Functional Interpolation Approach to Compute Periodic Orbits in the Circular-Restricted Three-Body Problem. Mathematics, 9.10.3390/math9111210 ↗
14. Musielak, Z., and Quarles, B. (2017). Three Body Dynamics and Its Applications to Exoplanets, Springer International Publishing. Available online: https://link.springer.com/content/pdf/10.1007/978-3-319-58226-9.pdf.10.1007/978-3-319-58226-9 ↗
15. Bischi, G.I., Panchuk, A., and Radi, D. (2022, February 09). Qualitative Theory of Dynamical Systems. Tools and Applications for Economic Modelling. Springer: Lectures Given at the Cost Training School on New Economic Complex Geography at Urbino, Italy, 17–19 September 2016. Available online: https://link.springer.com/book/10.1007/978-3-319-33276-5.10.1007/978-3-319-33276-5 ↗
16. Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions10.1007/s11075-016-0152-5 ↗
17. On the Newton-Raphson basins of convergence of the out-of-plane equilibrium points in the Copenhagen problem with oblate primaries10.1016/j.ijnonlinmec.2018.05.002 ↗
18. A class of methods for solving nonlinear simultaneous equations, mathematics of computation
19. Investigating the basins of convergence in the circular Sitnikov three-body problem with non-spherical primaries10.1007/s00601-018-1393-8 ↗
20. The perturbed restricted three-body problem with angular velocity: Analysis of basins of convergence linked to the libration points10.1016/j.ijnonlinmec.2020.103494 ↗
21. On the equilibria of the restricted three-body problem with a triaxial rigid body—I. Oblate primary10.1016/j.rinp.2021.103990 ↗
22. Basins of attraction of equilibrium points in the planar circular restricted five-body problem10.1007/s10509-017-3240-7 ↗
23. Villalibre, D., Herrero, A., Moraño, J.A., and Moll, S. (2022, January 14–16). Basins of Convergence in a Modified CR3BP. Proceedings of the Modelling for Engineering & Human Behaviour 2022 (MME&HB2022), València, Spain.
24. Effects of triaxiality of primaries on oblate infinitesimal in elliptical restricted three body problem10.1016/j.newast.2020.101538 ↗
25. Effect of oblateness and viscous force in the Robe’s circular restricted three-body problem10.1016/j.newast.2019.101280 ↗
26. On motion around the collinear libration points in the elliptic R3BP with a bigger triaxial primary10.1016/j.newast.2013.11.003 ↗
27. Research on the Stability of the Circular Restricted Three-body Problem with Radiation and Oblateness10.1016/j.chinastron.2019.11.006 ↗
28. The analysis of periodic orbits generated by Lagrangian solutions of the restricted three-body problem with non-spherical primaries10.1016/j.newast.2019.101287 ↗
29. Very Restricted Four-Body Problem10.1086/108151 ↗
30. On the convergence dynamics of the sitnikov problem with non-spherical primaries10.1007/s40819-019-0627-x ↗
31. NASA (2022, February 09). Sun Fact Sheet, Available online: https://cutt.ly/eWrGKBK.
32. NASA (2022, February 09). Mars Fact Sheet, Available online: https://cutt.ly/aWrG7u2.
33. Redd, N.T. (2022, February 09). Phobos: Facts About the Doomed Martian Moon. Space.com. Available online: https://cutt.ly/VWrJwuI.
34. Redd, N.T. (2022, February 09). Deimos: Facts About the Smaller Martian Moon. Space.com, Space. Available online: https://cutt.ly/5WrHXds.