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One of the important targets for the future space-based gravitational waveobservatory LISA is extreme mass ratio inspirals (EMRIs), where long andaccurate waveform modeling is necessary for detection and characterization.Modeling EMRI dynamics requires accounting for effects such as the ones inducedby an external tidal field, which can break integrability at resonances andcause significant dephasing. In this paper, we use a Newtonian analogue of aKerr black hole to study the effect of an external tidal field on the dynamicsand the gravitational waveform. We have developed a numerical framework thattakes advantage of the integrability of the background system to evolve it witha symplectic splitting integrator, and compute approximate gravitationalwaveforms to estimate the timescale over which the perturbation affects thedynamics. Comparing this timescale with the characteristic time under radiationreaction at resonance, we introduce a tool for quantifying the regime in whichtidal effects might be included when modeling EMRI gravitational waves. As anapplication of this framework, we perform a detailed analysis of the dynamicsat one resonance to show how different entry points into the resonance inphase-space can produce substantially different dynamics, and how one canestimate bounds for the parameter space where tidal effects may becomedominant. Such bounds will scale as $\varepsilon \gtrsim C \, q$, where$\varepsilon$ measures the strength of the external tidal field, $q$ is themass ratio, and $C$ is a number which depends on the resonance and the shape ofthe tide. We demonstrate how to estimate $C$ using our framework for the 2:3radial to polar frequency resonance in our model system. This framework canserve as a proxy for proper modeling of the tidal perturbation in the fullyrelativistic case.

Tidally-induced nonlinear resonances in EMRIs with an analogue model