High order symmetric algorithms for nonlinear dynamical systems with non-holonomic constraints

Shumin Man, Qiang Gao and Wanxie Zhong

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 212, issue C, 524-547

Abstract: Based on the Lagrange–d’Alembert principle and a modified Lagrange–d’Alembert principle, two kinds of symmetric algorithms with arbitrary high order are proposed for non-holonomic systems. The modified Lagrange–d’Alembert principle is constructed by adding an augment term to the Lagrange–d’Alembert principle, so that the non-holonomic constraints can be directly derived from variation. The high order algorithms are constructed by: (1) choosing control points to approximate generalized coordinates and Lagrange multipliers; (2) performing quadrature rules to approximate integrals; (3) choosing constraint points to satisfy non-holonomic constraints. The order of the presented algorithms is investigated numerically. The main factors to affect the accuracy of proposed algorithm were analyzed. Furthermore, the numerical algorithms are proven to be symmetric and can satisfy non-holonomic constraints with high precision.

Keywords: Non-holonomic systems; Symmetric; Lagrange–d’Alembert principle; Variational integrator; High-order methods (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475423002215
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:212:y:2023:i:c:p:524-547

DOI: 10.1016/j.matcom.2023.05.016

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().