Longitudinal dynamics of trains-a non-smooth approach

An efficient and straightforward algorithm for the integration of the constrained systems is developed in the present work. Some of the fundamental issues of contact dynamics are briefly reviewed. Considering Gauss' least constraint principle, an intuitive and effective computation method of the constraint forces is arrived at. The contact problem is solved by means of the generalized matrix inverse (GI) embedded in an appropriate algorithm and the numerical integration is event-driven. The method is applied to the study of train longitudinal dynamics which is essential for comfort and running safety. Due to the complexity of the phenomena and the presence of dry friction, the investigations have been carried out by numerical methods using regularization. Based on the non-smooth dynamics approach, in the present paper, a comprehensive model is presented. Set-value friction of Coulomb's law type is accounted for and motion equations are formulated as a differential inclusion. Application examples are presented. Simulations demonstrate the existence of specific phenomena like stick-slip and offset in the final equilibrium position. Computational efficiency is dramatically improved compared with previous models, while computation speed is increased by at least an order of magnitude. A wide class of problems may be solved using the present method, as is pointed out in the article.