Direct integration of the equations of multibody dynamics using central differences and linearization

Urkullu, Gorka; Bustos, Igor Fernández de; García-Marina, Vanessa; Uriarte, Haritz

doi:10.1016/j.mechmachtheory.2018.11.024

Cited by 8 publications

(7 citation statements)

References 42 publications

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“…This means that the timestep required for stability can easily be predicted with classical ODE theory. For example, methods as those presented in [34] exhibit predictable behavior. The main problem of these methods is that their stability limits the timestep required to solve the problem.…”

Section: Formulation Of the Problem Of Interest For This Investigationmentioning

confidence: 99%

“…This is the parameter that would define the stability limits if one accepts the values obtained for linear systems. For example, for a central difference method [34], one would reach:…”

Section: A Simple Example Of the Problem A Stiff Pendulummentioning

confidence: 99%

“…A similar approach was presented in [34], but applied to an explicit method. Due to the fact that explicit methods do not exhibit the stability behavior that implicit methods do, the approach in [34] cannot be used here.…”

Section: A New Approach For Solving the Problemmentioning

confidence: 99%

“…A more recent approach takes advantage of the so called structural integrators ( [34][35][36][37]). These methods are directly applied to the system expressed by eqns.…”

Section: Common Approaches For the Integration Of Constrained Systems...mentioning

confidence: 99%

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A non-damped stabilization algorithm for multibody dynamics

et al. 2021

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The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks (developed for ODEs) unusable. The appearance of these difficult-to-explain and unexpected problems leads to methods that arise heavy numerical damping for avoiding them. This has the undesired consequences of lack of convergence of the methods, along with a need of smaller stepsizes. In this paper a new approach is presented. The algorithm presented here allows us to avoid the interference of the constraints in the integration, thus allowing the linear criteria to be applied. In order to do so, the integrator is applied to a set of instantaneous minimal coordinates that are obtained through the application of the null space. The new approach can be utilized along with any integration method. Some experiments using the Newmark method have been carried out, which validate the methodology and also show that the method behaves in a predictable way if one considers linear stability criteria.

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Section: Formulation Of the Problem Of Interest For This Investigationmentioning

confidence: 99%

“…This is the parameter that would define the stability limits if one accepts the values obtained for linear systems. For example, for a central difference method [34], one would reach:…”

Section: A Simple Example Of the Problem A Stiff Pendulummentioning

confidence: 99%

Section: A New Approach For Solving the Problemmentioning

confidence: 99%

“…A more recent approach takes advantage of the so called structural integrators ( [34][35][36][37]). These methods are directly applied to the system expressed by eqns.…”

Section: Common Approaches For the Integration Of Constrained Systems...mentioning

confidence: 99%

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A non-damped stabilization algorithm for multibody dynamics

et al. 2021

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“…This method can conserve stability of long time simulation of the displacement, velocity and acceleration. Urkullu et al (2019) explored the direct central difference method for a solving multibody system, so that the equation could be solved directly without the of reducing the order. Terze et al (2015) analyzed the solving method of the first kind differential-algebra equation.…”

Section: Introductionmentioning

confidence: 99%

Comparison of long time simulation of Hamilton and Lagrange geometry dynamical models of a multibody system

Bai¹,

Ge²,

Xia³

2022

Journal of Theoretical and Applied Mechanics

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The geometry dynamical modeling method for a double pendulum is explored with the Lie group and a double spherical space method. Four types of Lagrange equations are built for relative and absolute motion with the above two geometry methods, which are then used to explore the influence of different expressions for motion on the dynamic modeling and computations. With Legendre transformation, the Lagrange equations are transformed to Hamilton ones which are dynamical models greatly reduced. The models are solved by the same numerical method. The simulation results show that they are better for the relative group than for the absolute one in long time simulation with the same numerical computations. The Lie group based result is better than the double spherical space one.

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