In this paper we develop an analytical set of equations to describe the motion of discrete dynamical systems subjected to holonomic and/or nonholonomic Pfaffian equality constraints. These equations are obtained by using Gauss’s Principle to recast the problem of the constrained motion of dynamical systems in the form of a quadratic programming problem. The closed-form solution to this programming problem then explicitly yields the equations that describe the time evolution of constrained linear and nonlinear mechanical systems. The direct approach used here does not require the use of any Lagrange multipliers, and the resulting equations are expressed in terms of two different classes of generalized inverses—the first class pertinent to the constraints, the second to the dynamics of the motion. These equations can be numerically solved using any of the standard numerical techniques for solving differential equations. A closed-form analytical expression for the constraint forces required for a given mechanical system to satisfy a specific set of nonholonomic constraints is also provided. An example dealing with the position tracking control of a nonlinear system shows the power of the analytical results and provides new insights into application areas such as robotics, and the control of structural and mechanical systems.
Skip Nav Destination
Article navigation
September 1993
Research Papers
Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss’s Principle
R. E. Kalaba,
R. E. Kalaba
Department of Eletrical Engineering and Biomedical Engineering, University of Southern California, Los Angeles, CA 90089-1453
Search for other works by this author on:
F. E. Udwadia
F. E. Udwadia
Civil Engineering and Decision Systems, University of Southern California, Los Angeles, CA 90089-1453
Search for other works by this author on:
R. E. Kalaba
Department of Eletrical Engineering and Biomedical Engineering, University of Southern California, Los Angeles, CA 90089-1453
F. E. Udwadia
Civil Engineering and Decision Systems, University of Southern California, Los Angeles, CA 90089-1453
J. Appl. Mech. Sep 1993, 60(3): 662-668 (7 pages)
Published Online: September 1, 1993
Article history
Received:
July 5, 1991
Revised:
October 30, 1991
Online:
March 31, 2008
Citation
Kalaba, R. E., and Udwadia, F. E. (September 1, 1993). "Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss’s Principle." ASME. J. Appl. Mech. September 1993; 60(3): 662–668. https://doi.org/10.1115/1.2900855
Download citation file:
Get Email Alerts
Related Articles
A New Model-Based Control Structure for Position Tracking in an Electro-Hydraulic Servo System With Acceleration Constraint
J. Dyn. Sys., Meas., Control (December,2017)
Hamiltonian Mechanics for Functionals Involving Second-Order Derivatives
J. Appl. Mech (November,2002)
Model Following Adaptive Sliding Mode Tracking Control Based on a Disturbance Observer for the Mechanical Systems
J. Dyn. Sys., Meas., Control (May,2018)
Path Following and Shape Morphing With a Continuous Slender Mechanism
J. Dyn. Sys., Meas., Control (October,2015)
Related Proceedings Papers
Related Chapters
Feedback-Aided Minimum Joint Motion
Robot Manipulator Redundancy Resolution
Manipulability-Maximizing SMP Scheme
Robot Manipulator Redundancy Resolution
Dynamic Ordinary Differential Equation Modeling of Stock Market Prediction with Gene Expression Programming
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3