Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations
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...
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| Format: | Article |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/6/1510 |
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| author | Lina Zhang Xiaoting Rui Jianshu Zhang Junjie Gu Xizhe Zhang |
| author_facet | Lina Zhang Xiaoting Rui Jianshu Zhang Junjie Gu Xizhe Zhang |
| author_sort | Lina Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T06:13:53Z |
| format | Article |
| id | doaj.art-f54f51e50e114e129928d3ec121215f9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:53Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f54f51e50e114e129928d3ec121215f92023-11-17T12:29:39ZengMDPI AGMathematics2227-73902023-03-01116151010.3390/math11061510Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint ViolationsLina Zhang0Xiaoting Rui1Jianshu Zhang2Junjie Gu3Xizhe Zhang4Institute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, ChinaInstitute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, ChinaInstitute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, ChinaInstitute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, ChinaInstitute of Launch Dynamics, Nanjing University of Science & Technology, Nanjing 210094, ChinaThe 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.https://www.mdpi.com/2227-7390/11/6/1510constraint violation correctiondirect correction methodenergy constraintsemi-analysis |
| spellingShingle | Lina Zhang Xiaoting Rui Jianshu Zhang Junjie Gu Xizhe Zhang Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations Mathematics constraint violation correction direct correction method energy constraint semi-analysis |
| title | Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations |
| title_full | Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations |
| title_fullStr | Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations |
| title_full_unstemmed | Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations |
| title_short | Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations |
| title_sort | exploring energy in the direct correction method for correcting geometric constraint violations |
| topic | constraint violation correction direct correction method energy constraint semi-analysis |
| url | https://www.mdpi.com/2227-7390/11/6/1510 |
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