  In the last decades, the dynamical studies around compact objects became a
subject of active research, partially motivated by the observed differences in
the profiles of the gravitational waves depending on the dynamics of the
system. In this work, via the Poincar\'e section method, we conduct a thorough
numerical analysis of the dynamical behavior of geodesics around Chazy-Curzon
metrics. As the main result, we find only regular motions for the geodesics in
all cases, which suggest the existence of the so-called Carter's constant in
this kind of exact solutions. Moreover, our simulations indicate that in the
two-particle Chazy-Curzon solution, some oscillatory motions take place as in
the classical MacMillan problem.
