Time elements in rectangular coordinates

In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerianorbital elements. We give here the corresponding time elements in terms ofrectangular coordinates. Extensive references are given in the previous paper and will be omitted here.We present additional numerical experiments comparing the use of time elementsand time transformationstogether with the use of time transformationsalone. The results indicate a reduction in computational error when time elements are used.