A Forward Dynamics Algorithm for State- and Phase-Space Based Simulations of Multibody Systems

摘要

In this work, we will focus on the dynamics of mechanical systems that can be modelled as an assembly of rigid bodies. Such multi-rigid-body models can also represent flexible systems if the effects of flexibility can be considered using discrete springs and dashpots connecting some of the rigid bodies. The solution of the forward dynamics problem is in the core of the development of efficient simulation algorithms. The configuration of a multibody system can be described by generalized coordinates, which can be written as the elements of array q . These can represent a minimum- or a redundant set of generalized coordinates. The first time derivatives of the generalized coordinates are called generalized velocities q, and the second time derivatives are the generalized accelerations q. The forward dynamics problem is usually interpreted as the determination of the generalized accelerations under the action of given applied forces/moments and initial conditions. This also indicates the almost exclusive use of acceleration-based formulations in computational multibody dynamics. Acceleration-based formulations can also be called the Lagrangian approach The resulting simulation formulation is based on either a state-space or a descriptor representation. Very few attempts have been made to establish algorithms for phase-space based simulations of general multi-rigid-body systems. Phase-space based simulations are associated with a forward dynamics formulation based on the time-rate of change of generalized momenta. Such formulations can also be called as the Hamiltonian approach. In this work, we will describe a new forward dynamics algorithm that can be used for both state- and phase-space based approaches. In this brief paper, we limit our discussion to a general open-loop chain of bodies.