Revisiting parallel car parking problem

Among many physical and mechanical engineering problems, parallel car parking has drawn the attention of many researchers as it shows how methods of Lie algebra and differential geometry can be applied elegantly to explain the behavior of such a system. In this paper we have reviewed some aspects of this problem in this context and analyse the stability and controllability of such a system by some unconventional integrators like Kahan and Lie trotter integrator. At the same time we have also given the results obtained through conventional Runge Kutta integrator to see a comparison.