In this work, the existence of symmetric periodic solutions of the Sitnikov problem was studied. Analytical solutions were obtained for the homogenous equation. The complementary function thus obtained, confirmed the existence of periodic solution. Further test for periodicity was carried out using the Bendixson Criterion. Due to the high nonlinear nature of the equation, Runge-Kutta fourth-order and Euler methods were again used to obtain an approximate solution which was unbounded and were compared with the analytical solution for the interval of eccentricities. Numerical simulation was obtained using MATCAD which extend some results in literature.
OKO, O (2022). Existence Of Symmetric Periodic Solutions In The Sitnikov Problem. Repository.mouau.edu.ng: Retrieved Jan 26, 2023, from https://repository.mouau.edu.ng/work/view/existence-of-symmetric-periodic-solutions-in-the-sitnikov-problem-7-2
OKO, OKO. "Existence Of Symmetric Periodic Solutions In The Sitnikov Problem" Repository.mouau.edu.ng. Repository.mouau.edu.ng, 28 Nov. 2022, https://repository.mouau.edu.ng/work/view/existence-of-symmetric-periodic-solutions-in-the-sitnikov-problem-7-2. Accessed 26 Jan. 2023.
OKO, OKO. "Existence Of Symmetric Periodic Solutions In The Sitnikov Problem". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 28 Nov. 2022. Web. 26 Jan. 2023. < https://repository.mouau.edu.ng/work/view/existence-of-symmetric-periodic-solutions-in-the-sitnikov-problem-7-2 >.
OKO, OKO. "Existence Of Symmetric Periodic Solutions In The Sitnikov Problem" Repository.mouau.edu.ng (2022). Accessed 26 Jan. 2023. https://repository.mouau.edu.ng/work/view/existence-of-symmetric-periodic-solutions-in-the-sitnikov-problem-7-2