The intermediate anomaly

Theory compression with elliptic functions

“…His idea is that One views the mean (true, eccentric) anomaly ... as the elliptic amplitude of a new (independent) variable' (see Nacozy, 1977). Unfortunately, this idea was related to the Hansen method of partial anomalies for the analytical representation of cometary motion.…”

“…It should be added that similar elliptic anomalies based on the transformation of the true anomaly ν instead of the eccentric anomaly g were introduced earlier by Bond and Janin (1981) and Nacozy (1977) to improve the efficiency of the numerical integration of highly eccentric orbits. In such a way all suggestions by Gylden mentioned above are now realized.…”

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…”

“…To settle these problems and obtain an acceptable precision, we can use several techniques [14] such as the choice of a very small uniform step, a variable step, and finally a change of the temporal variable so that a better temporal distribution of positions is obtained on the orbit near the perigee where the speed of the satellite is faster without reducing excessively the concentration of positions in the perigee, where the curvature, as well as in the perigee, is maximum. The problem of reparameterization of the temporal variable has been studied by several author [2,4,7,10,11] using several kinds of anomalies.…”

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

“…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. The constant factor α reads α = µ −1/2 (1 + e 2 ) 1/2 .…”