BOUNDEDNESS AND PERIODIC ORBITS IN THE STARK PROBLEM

. The Stark problem is a straightforward extension of the Kepler problem, with the addition of a constant perturbation. However, the resulting solution expressions are highly complex, making it difficult to intuitively comprehend the properties of the solutions. In this article, we focus on finding simpler and clearer ways to understand these solutions. We first establish equivalent conditions for boundedness through several common invariants in the Stark system. Furthermore, we reveal the existence of a sequence of periodic orbits and provide an intuitive, detailed description of their properties, particularly offering elegant and concise results for the brake solution. Finally, we attempt to apply variational methods to analyze the variational construction of these solutions.