On the use of Lie group time integrators in multibody dynamics

in Journal of Computational and Nonlinear Dynamics (2010), 5(3), 031002

This paper proposes a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parameterization problem. As an ... [more ▼]

This paper proposes a family of Lie group time integrators for the simulation of flexible multibody systems. The method provides an elegant solution to the rotation parameterization problem. As an extension of the classical generalized-alpha method for dynamic systems, it can deal with constrained equations of motion. Second-order accuracy is demonstrated in the unconstrained case. The performance is illustrated on several critical benchmarks of rigid body systems with high rotation speeds and second order accuracy is evidenced in all of them, even for constrained cases. The remarkable simplicity of the new algorithms opens some interesting perspectives for real-time applications, model-based control and optimization of multibody systems. [less ▲]

The generalized-alpha scheme as a linear multistep integrator: Toward a general mechatronic simulator

in Journal Of Computational And Nonlinear Dynamics (2008), 3(4), 041007

This paper presents a consistent formulation of the generalized-alpha time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a nonconstant mass matrix, controller ... [more ▼]

This paper presents a consistent formulation of the generalized-alpha time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a nonconstant mass matrix, controller dynamics; and kinematic constraints. The theoretical background relies on the analogy with linear multistep formulas, which leads to elegant results related to consistency, order conditions for constant and variable step-size methods, as well as global convergence. Those results are illustrated for a controlled spring-mass system, and the method is also applied for the simulation of a vehicle semi-active suspension. [less ▲]