# Symbolic Multibody Methods for Real-Time Simulation of Railway Vehicles

## TL;DR

This paper demonstrates the use of advanced symbolic multibody methods to accurately and efficiently simulate complex railway vehicles in real-time without simplifications, achieving high computational performance.

## Contribution

It introduces a symbolic modeling approach for railway vehicles that handles complex contact forces and stiff dynamics efficiently in real-time.

## Key findings

- Achieved real-time simulation with 256 μs CPU time per 1 ms step.
- Successfully modeled creep forces using symbolic implementation of the Kalker model.
- Demonstrated no need for model simplifications while maintaining accuracy.

## Abstract

In this work, recently developed state-of-the-art symbolic multibody methods are tested to accurately model a complex railway vehicle. The model is generated using a symbolic implementation of the principle of the virtual power. Creep forces are modeled using a direct symbolic implementation of the standard linear Kalker model. No simplifications, as base parameter reduction, partial-linearization or look-up tables for contact kinematics, are used. An Implicit-Explicit integration scheme is proposed to efficiently deal with the stiff creep dynamics. Hard real-time performance is achieved: the CPU time required for a very stable 1 ms integration time step is 256 {\mu}s.