The well known Euler-Lagrange equations of motion for constrained variational problems are derived using the principle of virtual work. These equations are used in the modelling of multibody systems and result in differential-algebraic equations of high index. Here they concern an N-link pendulum, a heavy aircraft towing truck and a heavy off-highway track vehicle. The differential-algebraic equation is cast as an ordinary differential equation through differentiation of the constraint equations. The resulting system is computed using the integration routine LSODAR, the Euler and fourth order Runge-Kutta methods. The difficulty to integrate this system is revealed to be the result of many highly oscillatory forces of large magnitude acting on many bodies simultaneously. Constraint compliance is analyzed for the three different integration methods and the drift of the constraint equations for the three different systems is shown to be influenced by nonlinear contact forces.
Numerical Computation of Differential-Algebraic Equations for Non-Linear Dynamics of Multibody Systems Involving Contact Forces
Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received Mar. 1999. Associate Editor: H. Lankarani.
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Fox, B., Jennings, L. S., and Zomaya, A. Y. (March 1, 1999). "Numerical Computation of Differential-Algebraic Equations for Non-Linear Dynamics of Multibody Systems Involving Contact Forces ." ASME. J. Mech. Des. June 2001; 123(2): 272–281. https://doi.org/10.1115/1.1353587
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