The main result of this paper is the proof of the stability of translating states for a system of n self-propelled agents governed by \(\ddot{r}_k = (\alpha -\beta |\dot{r}_k|^2)\dot{r}_k-\left[ \frac{\gamma }{n}\sum _{j=1}^n(r_k-r_j)+\frac{1}{n}\sum _{j=1}^n \nabla {\textbf {U}}_H(r_k-r_j)\right] \) , where \({\textbf {U}}_H\) has higher-order terms of a radial interaction potential, \(r_k\in \mathbb {R}^2\) . In numerical simulations, except for weak coupling, a large set of initial conditions lead to velocity alignment and convergence of the distances between agents to zero, a limiting configuration called translating state. Assuming that \(\gamma \) exceeds a small threshold, we prove that every solution starting near a translating state asymptotically approaches a nearby translating state. We work in a non-inertial frame moving with the center of mass, which lags behind rectilinear motion by \(\ln t\) . The oscillations normal to the motion decay at a rate of \(1/ \sqrt{t}\) , resembling those of systems with almost periodic coefficients and cubic nonlinearities. We provide sufficient conditions on the means of the coefficient functions that guarantee the asymptotical stability of the origin in such systems. We quantify the convergence rates for the directional drift, mean field speed, and the coupling threshold.
