Secular resonances as a source of dynamic chaoticity in the long-term orbital evolution of uncontrolled satellites

Analysis on the long-term dynamical evolution of the inclined geosynchronous orbits in the Chinese BeiDou navigation system

“…Then from which we can also make some preliminary explanation on the long-term variation of eccentricity of these IGSO satellites and the increase of the eccentricity of the corresponding IGSO satellites in the long-term evolution. But the IGSO satellites with high initial inclination may go through several other different resonances during the evolution (Bordovitsyna et al, 2014) and those resonances locate quite close to each other, especially in large eccentricity region. The simple analysis is not adequate, and it needs more depth researches.…”

“…Ulivieri et al (2013) analyzed the variation of inclination and the precession period of orbital plane of near circular GEO satellites (including near circular IGSO satellites with high inclination) as functions of initial inclination and initial longitude of ascending node; but they only presented some specific figures to show the variation range of inclination and the precession period of orbital plane without the explicitly analytical expressions. Bordovitsyna et al (2014) studied the long-term orbital evolution of BeiDou-IGSO satellites by means of mean exponential growth of nearby orbits (MEGNO) analysis, and pointed out that the secular resonances affect the motions of BeiDou-IGSO satellites significantly. How does the semimajor axis a and the inclination i of these IGSO satellites with the inclination of about 55°in the Chinese BeiDou navigation system vary?…”

The effect of secular resonances on the long-term orbital evolution of uncontrolled near-Earth objects

“…This effect appears after the eccentricity increases up to 0.6. See detailes in (Bordovitsyna et al 2014).…”

“…The superposition of several secular resonances or orbital and secular resonances are the source of randomness in the motion of objects. To study the effect of secular resonances on uncontrolled near-Earth objects we use a numerical-analytical approach consisting in (Bordovitsyna et al 2012): − identifying the secular resonances based on an analytical method on condition that the third body orbit is an ellipse with revolving nodal and apsidal lines; − numerical modeling the long-term orbital evolution using the software package Numerical Model of Motion of Satellite Systems (Bordovitsyna et al 2009) realized in a parallel programming environment at the Tomsk State University computing cluster; − MEGNO-analysis of dynamic evolution of objects (Cincotta et al 2003).A complete set of 29 low order resonance relations has been presented in Bordovitsyna et al (2014). This set may be considered as a small modification of the resonance relation list obtained by Cook (1962) and by Hughes (1980Hughes ( , 1981.…”

“…A complete set of 29 low order resonance relations has been presented in Bordovitsyna et al (2014). This set may be considered as a small modification of the resonance relation list obtained by Cook (1962) and by Hughes (1980Hughes ( , 1981.…”