To calculate the period of a trajectory for a second order nonlinear ordinary differential equation (ODE) with specified initial conditions without directly solving the ODE, numerical methods such as Runge-Kutta can be employed. The discussion emphasizes that using numerical integration techniques is generally acceptable for estimating the period, even if it involves approximating the solution. Participants express uncertainty about the terminology of "solving" the ODE versus using numerical methods, seeking clarification on whether these methods align with the goal of determining the period without a full analytical solution. Additionally, references to specific numerical methods from related literature are mentioned, indicating a desire for guidance on unfamiliar techniques.
