Motion and Vibration of a Moving Body on the 3D Trajectory Considering Running Resistance

The motion and vibration of a moving body running on the complicated 3 dimensional trajectory considering the running resistance are investigated in this paper. A roller coaster is treated with here as the concrete example of a moving body. The equations of motion of a roller coaster in which a trajectory and a vehicle are coupled are derived by using the differential-algebraic equation (DAE). The dynamic behavior of a roller coaster which moves forward due to the gravity acceleration neglecting the running resistance has been reported in our former papers. In this paper, we take the effect of an air resistance and a rolling resistance into consideration. The influences of these resistances on the required time from the starting point to the arriving one and the vibration response of a vehicle are investigated. Moreover, it is shown that the numerical solutions have a better coincidence with the experimental results which have been obtained by measuring an actual roller coaster.