According　to　Lagrange＇s　equation,　the　governing　equation　for　a　base　isolated　structural　system　was　presented,　with　a　variable　friction　coefficient　RFPS　(the　rolling　friction　pendulum　system)　bearing　on　arbitrary　curves.　Its　solution　was　presented　with　software　prepared　from　MATLAB　language.　Results　show　that　the　variable　friction　coefficient　RFPS　might　result　in　complication　of　structural　dynamic　responses.　It　is　noticed　that　seismic　mitigation　efficiency　for　the　variable　friction　coefficient　is　close　to　that　for　the　high　friction　coefficient,　but　with　notable　disadvantages　to　the　lower　friction　coefficient.　As　RFPS　slipper　transits　from　the　low-　to　the　high-friction　area,　the　structural　system　could　exhibit　noticeable　whipping　effect,　which　will　amplify　story　accelerations.　It　is　suggested　that　lower　friction　coefficient　FPS　bearings,　instead　of　variable　friction　coefficient　RFPS　bearings,　should　be　applied.