Analyzing QPOs and dynamics with trajectories around charged Horndeski black hole

In this study, we investigate the motion of neutral test particles in the space-time of a spherically symmetric charged Horndeski black hole. By employing the effective potential method, we analyze the conditions for the stability of circular orbits confined to the equatorial plane. Explicit mathematical relations for the energy and angular momentum of test particles are obtained as functions of the black hole parameters, highlighting the role of charge and scalar coupling in orbital dynamics. We further examine the behavior of the effective force exerted on the particles and determine the position of the innermost stable circular orbit. To complement the analytical results, we numerically solve the equations of motion and visualize the trajectories of test particles under different configurations. The study is extended to include small perturbations around stable orbits, from which we derive the radial, polar, and azimuthal epicyclic frequencies. Additionally, we compute the periastron precession frequency and explore its dependence on black hole parameters. The overall analysis demonstrates that the dynamical properties of particles are highly sensitive to the characteristics of the black hole, offering deeper insights into the influence of Horndeski modifications on relativistic motion.