Accurate computation of highly eccentric satellite orbits

Study of Errors in the Integration of the Two Body Problem Using Generalized Sundman’s Anomalies

“…Later Nacozy [6,11] extended this transformation to a more general dt D C˛r˛d, such family of transformations includes the mean, eccentric and true anomalies for values of˛D 0; 1; 2 and appropriate values of C˛ [9]. From the above mentioned family Lopez [9] introduces the concept of Sundman's generalized anomaly «˛as a function «˛.M / so that…”

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

“…77-78), with a consequent uniformization and reduction of the local truncation error over one orbital revolution (Velez 1974;Feagin & Mikkilineni 1976;Velez & Hilinski 1978). Such uniformization has the important advantage of allowing the use of fixed step size numerical methods even in the numerical integration of highly eccentric orbits (Janin 1974;Velez 1974) thus avoiding resorting to more sophisticated, and in some cases less efficient, variable step size schemes.…”

“…The Stiefel-Scheifele time element has also been proposed in combination with the Newtonian equations of motion (Baumgarte 1972;Baumgarte & Stiefel 1974). Numerical tests show that the integration of the stabilized equations in Cartesian coordinates equipped with a time element can be as accurate as a regularized set of elements (Janin 1974). An interesting property of the Stiefel-Scheifele time element is that it can be incorporated as a coordinate into several canonical sets of variables by means of a canonical transformation applied in the extended phase space (Ferrándiz & Sansaturio 1995).…”

Regularization in Astrodynamics: applications to relative motion, low-thrust missions, and orbit propagation = Regularización en Astrodinámica: aplicaciones al movimiento relativo, misiones de bajo empuje, y propagación de órbitas

“…Many regularization methods are based on the transformation n = 1. Some examples are the formulations by Levi-Civita (1904, 1906, 1920 and later extended by Kustaanheimo and Stiefel (1965), or alternative methods by Sperling (1961), Burdet (1967), Janin (1974), Bond and Gottlieb (1989), Bond (1990), Roa and Peláez (2015d) and Baù et al (2015), among others. The case n = 3/2 was explored by Nacozy (1977), who coined the term intermediate anomaly for referring to the fictitious time in this case.…”

“…This control term appears recursively in the literature and it is sometimes referred to as the Poincaré term (Baumgarte and Stiefel, 1974;Janin, 1974 Figure 2.3 shows the difference in accuracy between integrating Eq. (2.10) and Eq.…”