Symbolic methods for modelling rail vehicle systems

In developing and analysing mathematical models for complex systems such as railway vehicles, the analyst is faced with a number of challenges. The derivation of the equations themselves can be a tedious and error-prone task. The selection of analysis techniques suited to the nature of the problem is a big factor in being able to obtain meaningful results. Computerized symbolic tools such as MAPLE offer great possibilities. These tools are easily integrable with powerful numerical software packages that can be used to provide numerical solutions if necessary. Algorithms to derive symbolic equation's of motion for dynamic systems have progressed greatly in recent times. For a model with several degrees of freedom, a computer can formulate the equations of motion and transcribe them into a numeric integration program much more rapidly and accurately than a person can. Because the equations are in symbolic form, it is possible to perform parametric studies without modifying the simulation code, and the simulation can easily be linearized about a given datum. This paper presents the use of symbolic tools for the analysis of railway-vehicle systems. An algorithm that automates the development of equations of motion for railway vehicles in MAPLE is presented. A series of examples are presented which include applications to a non-linear model of a wheelset, a conventional vehicle and a series of articulated trainsets. Numerical simulation and linear stability analysis of these models are conducted in the commercial simulation package MATLAB and the results presented for the different examples.