DAE time integration for real-time applications in multi-body dynamics The equations of motion of multi-body systems with kinematically closed loops are given by differential-algebraic equations (DAE). Real-time applications like hardware-in-the-loop testbeds or driving simulators require appropriate integration methods that can solve the nonlinear constraints without exceeding an a priori fixed number of calculation steps. Partitioned linear-implicit Euler methods can be extended by appropriate stabilization techniques to keep the error in the constraints bounded for arbitrary time intervals. These methods need a fixed low number of operations for each time step. One simplified Newton step for the projection onto the constraint manifold can prevent the drift-off for arbitrary time intervals if the stepsize is sufficiently small. Selected methods were successfully implemented in the commercial vehicle simulation package veDYNA to improve substantially the simulation capabilities for vehicle-trailer coupling.

References in zbMATH (referenced in 10 articles , 1 standard article )

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  1. Wang, Yulei; Gao, Jinwu; Li, Kai; Chen, Hong: Integrated design of control allocation and triple-step control for over-actuated electric ground vehicles with actuator faults (2020)
  2. Burger, Michael; Gerdts, Matthias: A survey on numerical methods for the simulation of initial value problems with sDAEs (2017)
  3. Carpinelli, Mariano; Gubitosa, Marco; Mundo, Domenico; Desmet, Wim: Automated independent coordinates’ switching for the solution of stiff DAEs with the linearly implicit Euler method (2016)
  4. Bursi, O. S.; Wang, Z.; Jia, C.; Wu, B.: Monolithic and partitioned time integration methods for real-time heterogeneous simulations (2013)
  5. Burgermeister, Bernhard; Arnold, Martin; Eichberger, Alexander: Smooth velocity approximation for constrained systems in real-time simulation (2011)
  6. Fritzkowski, Paweł; Kamiński, Henryk: Dynamics of a rope modeled as a discrete system with extensible members (2009)
  7. Arnold, Martin; Burgermeister, Bernhard; Eichberger, Alexander: Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs (2007)
  8. Kim, Sung-Soo; Jeong, Wanhee: Subsystem synthesis method with approximate function approach for a real-time multibody vehicle model (2007)
  9. Valasek, Michael; Sika, Zbynek; Vaculin, Ondrej: Multibody formalism for real-time application using natural coordinates and modified state space (2007)
  10. Burgermeister, B.; Arnold, M.; Esterl, B.: DAE time integration for real-time applications in multi-body dynamics (2006)