The Hermite–Obreshkov–Padé (HOP) method of numerical integration is applicable to stiff systems of differential equations, where the linearization has large range of eigenvalues. A practical implementation of HOP requires the ability to determine high-order time derivatives of the system variables. In the case of a constrained multibody dynamical system, the power series solution for the kinematic differential equation is the foundation for an algorithmic differentiation (AD) procedure determining those derivatives. The AD procedure is extended in this paper to determine rates of change in the time derivatives with respect to variation in the position and velocity state variables of the multibody system. The coefficients of this variation form the Jacobian matrix required for Newton–Raphson iteration. That procedure solves the implicit relations for the state variables at the end of each integration time step. The resulting numerical method is applied to the rotation of a dynamically unbalanced constant-velocity (CV) shaft coupling, where the deflection angle of the output shaft is constrained to low levels by springs of high rate and damping.
Skip Nav Destination
Article navigation
November 2014
Research-Article
Numerical Solution of Stiff Multibody Dynamic Systems Based on Kinematic Derivatives
Paul Milenkovic
Paul Milenkovic
Department of Electrical
and Computer Engineering,
e-mail: phmilenk@wisc.edu
and Computer Engineering,
University of Wisconsin-Madison
,1415 Engineering Drive
,Madison, WI 53706
e-mail: phmilenk@wisc.edu
Search for other works by this author on:
Paul Milenkovic
Department of Electrical
and Computer Engineering,
e-mail: phmilenk@wisc.edu
and Computer Engineering,
University of Wisconsin-Madison
,1415 Engineering Drive
,Madison, WI 53706
e-mail: phmilenk@wisc.edu
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 25, 2012; final manuscript received June 30, 2014; published online August 8, 2014. Assoc. Editor: YangQuan Chen.
J. Dyn. Sys., Meas., Control. Nov 2014, 136(6): 061001 (9 pages)
Published Online: August 8, 2014
Article history
Received:
May 25, 2012
Revision Received:
June 30, 2014
Citation
Milenkovic, P. (August 8, 2014). "Numerical Solution of Stiff Multibody Dynamic Systems Based on Kinematic Derivatives." ASME. J. Dyn. Sys., Meas., Control. November 2014; 136(6): 061001. https://doi.org/10.1115/1.4028049
Download citation file:
Get Email Alerts
Cited By
Data-Driven Tracking Control of a Cushion Robot With Safe Autonomous Motion Considering Human-Machine Interaction Environment
J. Dyn. Sys., Meas., Control (July 2025)
Dynamic Obstacle Avoidance Strategy for High-Speed Vehicles Via Constrained Model Predictive Control and Improved Artificial Potential Field
J. Dyn. Sys., Meas., Control (July 2025)
An Adaptive Sliding-Mode Observer-Based Fuzzy PI Control Method for Temperature Control of Laser Soldering Process
J. Dyn. Sys., Meas., Control
Related Articles
Multi-Integral Method for Solving the Forward Dynamics of Stiff Multibody Systems
J. Dyn. Sys., Meas., Control (September,2013)
Projective Constraint Stabilization for a Power Series Forward Dynamics Solver
J. Dyn. Sys., Meas., Control (May,2013)
Solution of the Forward Dynamics of a Single-loop Linkage Using Power Series
J. Dyn. Sys., Meas., Control (November,2011)
Series Solution for Finite Displacement of Single-Loop Spatial Linkages
J. Mechanisms Robotics (May,2012)
Related Proceedings Papers
Related Chapters
Feedback-Aided Minimum Joint Motion
Robot Manipulator Redundancy Resolution
Cellular Automata: In-Depth Overview
Intelligent Engineering Systems through Artificial Neural Networks, Volume 20
Fundamentals of Finite Element and Finite Volume Methods
Compact Heat Exchangers: Analysis, Design and Optimization using FEM and CFD Approach