Chariklo , the first minor body discovered to possess rings, has attracted widespread attention regarding the dynamics of its ring system. This paper investigates the influence of Chariklo's equatorial ellipticity and rotational motion on the orbital motion of ring particles within its gravitational field. By constructing the Lagrange function based on the kinematic formulation of the complete non-conservative system equations of motion, we derive the system's Lagrange function. The discrete variational principle is then applied to establish a discrete orbital dynamics model for the system, and the orbital structure and dynamical mechanisms of ring particles are further explored. Through Poincaré section analysis, two types of periodic orbits are identified: the first kind of periodic orbit and the 1:3 resonant periodic orbit. By studying the characteristics of these two types of periodic orbits, we establish the connection between Chariklo's inner and outer rings and these orbits. It is also demonstrated that, compared with the Runge-Kutta method, the discrete variational method exhibits superior energy conservation and structure-preserving capabilities, making it more suitable for accurately simulating and analyzing such complex dynamical systems over long timescales with better orbital stability. The results indicate that particles in Chariklo's inner ring may reside on the first kind of periodic orbits—which satisfy specific radial oscillation amplitude ranges—and their adjacent quasi-periodic orbits, or possibly on 1:3 resonant orbits. In contrast, particles in the outer ring are distributed solely on the first kind of periodic orbits and their surrounding quasi-periodic orbits.