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This paper investigates the dynamic disturbances affecting weapon systems mounted on unmanned ground vehicles (UGVs), which pose a significant challenge in maintaining aiming accuracy when moving across uneven terrain. These disturbances arise from terrain-induced vibrations, complex hull movements, suspension-induced vibrations, and cross-inertial interactions between the gun barrel and the turret, particularly under asymmetrical road excitations. This research aims to develop a comprehensive mathematical model describing the dynamic disturbances caused by mass imbalances and cross-inertial effects in weapon-UGV systems and to analyse the influence of asymmetrical and non-uniform road surfaces on weapon system vibrations. The proposed nonlinear dynamic model is constructed using Euler rotation matrices and coordinate transformation methods, incorporating suspension-induced disturbances. An uneven road model with varying roughness heights between the left and right sides and asymmetrical profiles was introduced, including sequential semi-sinusoidal, trapezoidal, and rectangular ridge shapes to represent battlefield-like terrain conditions. The governing equations were solved in MATLAB-Simulink to evaluate weapon vibrations, angular deviations, and disturbance torques. The simulation results showed that asymmetrical road excitation significantly amplified the disturbances to the weapon system during aiming. A scaled UGV model was used to conduct experiments on vehicle body vibrations while moving over a rough terrain section, assessing the effect of suspension and uneven road surfaces on the weapon system. The results demonstrate that the developed dynamic disturbance model provides a solid basis for future stabilisation and compensation control strategies. It improves the firing accuracy of weapon systems mounted on unmanned ground vehicles operating in real-world conditions.