Motion and Vibration Analysis for Multi-Vehicles of a Roller Coaster on the 3D Trajectory

The motion and vibration for multi-vehicles of a roller coaster which move on the complicated three-dimensional trajectories are investigated. A roller coaster is treated with here as a concrete example of moving body. By using differential algebraic equations (DAE), the simulation method for moving bodies on 3D trajectory is proposed in this paper. In the previous papers, the simulation method using s-u-z coordinate for a single vehicle has been shown. In this paper, the analysis method which uses the global coordinate xg-yg-zg is shown. In addition, the simulation method for multi-vehicles of a roller coaster is proposed. In order to solve the instability of the simulation analysis, the stabilization method proposed by Baumgarte is adopted. When all of connecting points are taken into consideration as constraint conditions, it is found to be too severe, and some play is necessary at connecting points for practical applications to an actual roller coaster. Lastly, the validity of the proposed simulation method by comparing with the experiment which have been reported in previous paper is examined.