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Full-Text Articles in Dynamic Systems
Euler's Three-Body Problem, Sylvio R. Bistafa
Euler's Three-Body Problem, Sylvio R. Bistafa
Euleriana
In physics and astronomy, Euler's three-body problem is to solve for the motion of a body that is acted upon by the gravitational field of two other bodies. This problem is named after Leonhard Euler (1707-1783), who discussed it in memoirs published in the 1760s. In these publications, Euler found that the parameter that controls the relative distances among three collinear bodies is given by a quintic equation. Later on, in 1772, Lagrange dealt with the same problem, and demonstrated that for any three masses with circular orbits, there are two special constant-pattern solutions, one where the three bodies remain …
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the problem of resonance in a motion of a geocentric satellite is numerically investigated under the consolidated gravitational forces of the Sun, the Earth including Earth’s equatorial ellipticity parameter and Poynting-Robertson (P-R) drag. We are presuming that bodies lying on an ecliptic plane are the Sun and the Earth, and satellite on orbital plane. Resonance is monitored between satellite’s mean motion and average angular velocity of the Earth around the Sun, and also between satellite’s mean motion and equatorial ellipticity parameter of the Earth. We also perform a systematic and thorough analysis in an attempt to understand …
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag, Charanpreet Kaur, Binay K. Sharma, L. P. Pandey
Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag, Charanpreet Kaur, Binay K. Sharma, L. P. Pandey
Applications and Applied Mathematics: An International Journal (AAM)
The problem of resonance in a geocentric Satellite under the combined gravitational forces of the Sun and the Earth due to Poynting-Robertson (P-R) drag has been discussed in this paper with the assumption that all three bodies, the Earth, the Sun and the Satellite, lie in an ecliptic plane. Our approach differs from conventional ones as we have placed evaluated velocity of the Satellite in equations of motion.We observed five resonance points commensurable between the mean motion of the Satellite and the average angular velocity of the Earth around the Sun, out of which two resonances occur only due to …