A few Kozai-Lidov cycles with their distinctive signature of high-eccentricity (low 1 − e₁) spikes. On the right, the eccentricity and relative inclination are plotted against each other from t = 0 to t = 10000 yr, including the analytical prediction (based on the initial conditions and conservation of linear momentum in Equation C.2). The thickness of this line is due to numerical integration errors. Initial condition is a binary of masses m₁ = 1 M_Jup and m₂ = 1M_⊙, semimajor axis a₁ = 0.005 AU, and eccentricity e₁ = 0.001, orbited by a third body of mass m₃ = 10⁶M_⊙ at semimajor axis a₂ = 51.4 AU, eccentricity e₂ = 0.7, and relative inclination i_rel = 95°. Integration was done using a regularized Hermite integrator with a time-step parameter of η = 0.01.