The discrete null space method for the energy consistent integration of constrained mechanical systems: Part I: Holonomic constraints

By Peter Betsch. 2005

184 citations recorded by the source corpus.

The present work deals with energy consistent time stepping schemes for finite-dimensional mechanical systems with holonomic constraints. The proposed procedure is essentially based upon the following steps: Firstly, the index three differential-algebraic equations corresponding to the constrained mechanical system are directly discretized. Secondly, the discrete Lagrange multipliers are eliminated by using a discrete null space matrix. In many cases it is feasible to further reduce the number of unknowns by employing specific reparametrizations. The proposed method entails a number of advantageous features such as size-reduction and improved conditioning of the resulting system of algebraic equations. It is shown that the newly developed method is well-suited for both open-loop and closed-loop multibody systems.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/af5c49e6330c20330ad266a1dc0956ef69d7218b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Discrete mechanics and optimal control for constrained systems (2010, methodology): “This work combines two recently developed methods, namely the discrete null space method that is suitable ∗Correspondence to: S. Leyendecker, Aeronautics and Control and Dynamical Systems, California Institute of Technology, 1200 E. California Boulevard, Mail Code 107-81, Pasadena, CA 91125, U.S.A. ”
Towards bridging the gap between motion capturing and biomechanical optimal control simulations (2015, methodology): “The discrete Euler-Lagrange equations resulting from the stationary condition for the discrete action are reduced to minimal dimension using a discrete null space matrix P(qk) ∈ R29×7 and the nodal reparametrisation Fd resulting in (2), see [2, 10].”
Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems (2008, methodology): “For holonomic systems, Schiehlen [35] derived governing DAEs and ODEs, the Boltzmann-Hamel equations, as well as equations of motion based on a recursive approach.”
Energy-momentum conserving integration of multibody dynamics (2007, methodology): “The size of the algebraic system to be solved can be systematically reduced by applying the discrete null space method developed in reference [ 5 ].”
The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: multibody dynamics (2006, methodology): “The precursor work [ 1 ] will be subsequently referred to as Part I.”
A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems (2009, methodology): “In this context, the discrete null space method has been developed by the second author [28] to achieve a size-reduction along with an improved conditioning of the system to be solved.”