Use of the Non-Inertial Coordinates in the Analysis of Train Longitudinal Forces

A new three-dimensional non-linear train car coupler model is established,which takes into account the geometric nonlinearity due to the coupler and car body displacements.The proposed non-linear coupler model allows for arbitrary three-dimensional motion of the car bodies and captures kinetic degrees of freedom that are not captured using existing simpler models.By assuming the inertia of the coupler components negligible compared to the inertia of the car body,the system coordinates are partitioned into two distinct sets;inertial and non-inertial coordinates.The inertial coordinates that describe the car motion have inertia forces associated with them.The non-inertial coupler coordinates,on the other hand,describe the coupler kinetics and have no inertia forces associated with them.While the developed more-detailed coupler model captures the coupler kinetic degrees of freedom,it does not lead to an increase in the number of state equations,number of the system inertial coordinates,and number of constraint equations.Furthermore,by using this approach,one avoids having a system of stiff differential equations that can arise because of the relatively small coupler mass.Numerical results of simple train models are presented in order to demonstrate the use of the formulation developed in this paper.