Error analysis of forced discrete mechanical systems

by   Javier Fernandez, et al.

The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Essentially, we prove that when a discretization of contact order r of the Lagrangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over TQ, where we study the existence of flows, the construction and properties of discrete exact systems and the contact order of the flows (variational integrators) in terms of the contact order of the original systems. Then we use those results to derive the corresponding analysis for the analogous forced systems defined over Q× Q.


page 1

page 2

page 3

page 4


On the geometry of discrete contact mechanics

In this paper, we continue the construction of variational integrators a...

Discrete Hamilton-Jacobi theory for systems with external forces

This paper is devoted to discrete mechanical systems subject to external...

A hybrid discrete-continuum approach to model hydro-mechanical behaviour of soil during desiccation

Desiccation cracking in clayey soils occurs when they lose moisture, lea...

An Efficient Model Order Reduction Scheme for Dynamic Contact in Linear Elasticity

The paper proposes an approach for the efficient model order reduction o...

Parallel iterative methods for variational integration applied to navigation problems

Discrete variational methods have shown an excellent performance in nume...

From modelling of systems with constraints to generalized geometry and back to numerics

In this note we describe how some objects from generalized geometry appe...

Determination of Physical and Mechanical properties of Sugarcane Single-Bud Billet

Determining the physical and mechanical properties of sugarcane single-b...