Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations

Lina Zhang, Xiaoting Rui, Jianshu Zhang (), Junjie Gu and Xizhe Zhang
Additional contact information
Lina Zhang: Institute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, China
Xiaoting Rui: Institute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, China
Jianshu Zhang: Institute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, China
Junjie Gu: Institute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, China
Xizhe Zhang: Institute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, China

Mathematics, 2023, vol. 11, issue 6, 1-20

Abstract: The direct correction method is widely used for eliminating geometric constraint violations. This method involves iteratively adjusting the generalized coordinates, which are assumed to be consistent and remain so during the velocity-level corrections. However, the corrected generalized coordinates cause a significant effect on the velocity constraint violations. In this paper, simultaneously correcting both the generalized coordinates and velocities is proposed. A semi-analytic approach to solve the Jacobian matrix, which is used to correct the generalized coordinates and velocities, was employed. Further, the position level, velocity level, and energy constraint equations were corrected simultaneously to ensure that the corrected generalized coordinates and velocities complied with the dynamic equations. The corresponding semi-analytic Jacobian matrix was derived to solve the constraint equations. The methods were demonstrated to be effective using examples, with the simultaneous correction of position-level and velocity-level constraints showing the best results when combined with the energy correction.

Keywords: constraint violation correction; direct correction method; energy constraint; semi-analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1510/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1510/ (text/html)

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:gam:jmathe:v:11:y:2023:i:6:p:1510-:d:1102537

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().