Rotational k-cycle systems of order v<3k; another proof of the existence of odd cycle systems

We give an explicit solution to the existence problem for 1-rotational k-cycle systems of order v < 3k with k odd and v ≠ 2k + 1. We also exhibit a 2-rotational k-cycle system of order 2k + 1 for any odd k. Thus, for k odd and any admissible v < 3k there exists a 2-rotational k-cycle system of order v. This may also be viewed as an alternative proof that the obvious necessary conditions for the existence of odd cycle systems are also sufficient.