On the constraints violation in forward dynamics of multibody systems
Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial d...
Ausführliche Beschreibung
Autor*in: |
Marques, Filipe [verfasserIn] Souto, António P. [verfasserIn] Flores, Paulo [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2016 |
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Schlagwörter: |
Baumgarte stabilization method Augmented Lagrangian formulation Index-1 Lagrangian formulation |
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Übergeordnetes Werk: |
Enthalten in: Multibody system dynamics - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997, 39(2016), 4 vom: 29. Aug., Seite 385-419 |
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Übergeordnetes Werk: |
volume:39 ; year:2016 ; number:4 ; day:29 ; month:08 ; pages:385-419 |
Links: |
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DOI / URN: |
10.1007/s11044-016-9530-y |
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Katalog-ID: |
SPR016048539 |
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520 | |a Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. | ||
650 | 4 | |a Constraints violation |7 (dpeaa)DE-He213 | |
650 | 4 | |a Baumgarte stabilization method |7 (dpeaa)DE-He213 | |
650 | 4 | |a Penalty method |7 (dpeaa)DE-He213 | |
650 | 4 | |a Augmented Lagrangian formulation |7 (dpeaa)DE-He213 | |
650 | 4 | |a Index-1 Lagrangian formulation |7 (dpeaa)DE-He213 | |
650 | 4 | |a Coordinate partitioning method |7 (dpeaa)DE-He213 | |
650 | 4 | |a Mechanical energy |7 (dpeaa)DE-He213 | |
650 | 4 | |a Computational efficiency |7 (dpeaa)DE-He213 | |
650 | 4 | |a Forward dynamics |7 (dpeaa)DE-He213 | |
650 | 4 | |a Multibody systems |7 (dpeaa)DE-He213 | |
700 | 1 | |a Souto, António P. |e verfasserin |4 aut | |
700 | 1 | |a Flores, Paulo |e verfasserin |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Multibody system dynamics |d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 |g 39(2016), 4 vom: 29. Aug., Seite 385-419 |w (DE-627)271181087 |w (DE-600)1479537-1 |x 1573-272X |7 nnns |
773 | 1 | 8 | |g volume:39 |g year:2016 |g number:4 |g day:29 |g month:08 |g pages:385-419 |
856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11044-016-9530-y |z lizenzpflichtig |3 Volltext |
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10.1007/s11044-016-9530-y doi (DE-627)SPR016048539 (SPR)s11044-016-9530-y-e DE-627 ger DE-627 rakwb eng 600 ASE 50.32 bkl Marques, Filipe verfasserin aut On the constraints violation in forward dynamics of multibody systems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. Constraints violation (dpeaa)DE-He213 Baumgarte stabilization method (dpeaa)DE-He213 Penalty method (dpeaa)DE-He213 Augmented Lagrangian formulation (dpeaa)DE-He213 Index-1 Lagrangian formulation (dpeaa)DE-He213 Coordinate partitioning method (dpeaa)DE-He213 Mechanical energy (dpeaa)DE-He213 Computational efficiency (dpeaa)DE-He213 Forward dynamics (dpeaa)DE-He213 Multibody systems (dpeaa)DE-He213 Souto, António P. verfasserin aut Flores, Paulo verfasserin aut Enthalten in Multibody system dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 39(2016), 4 vom: 29. Aug., Seite 385-419 (DE-627)271181087 (DE-600)1479537-1 1573-272X nnns volume:39 year:2016 number:4 day:29 month:08 pages:385-419 https://dx.doi.org/10.1007/s11044-016-9530-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.32 ASE AR 39 2016 4 29 08 385-419 |
spelling |
10.1007/s11044-016-9530-y doi (DE-627)SPR016048539 (SPR)s11044-016-9530-y-e DE-627 ger DE-627 rakwb eng 600 ASE 50.32 bkl Marques, Filipe verfasserin aut On the constraints violation in forward dynamics of multibody systems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. Constraints violation (dpeaa)DE-He213 Baumgarte stabilization method (dpeaa)DE-He213 Penalty method (dpeaa)DE-He213 Augmented Lagrangian formulation (dpeaa)DE-He213 Index-1 Lagrangian formulation (dpeaa)DE-He213 Coordinate partitioning method (dpeaa)DE-He213 Mechanical energy (dpeaa)DE-He213 Computational efficiency (dpeaa)DE-He213 Forward dynamics (dpeaa)DE-He213 Multibody systems (dpeaa)DE-He213 Souto, António P. verfasserin aut Flores, Paulo verfasserin aut Enthalten in Multibody system dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 39(2016), 4 vom: 29. Aug., Seite 385-419 (DE-627)271181087 (DE-600)1479537-1 1573-272X nnns volume:39 year:2016 number:4 day:29 month:08 pages:385-419 https://dx.doi.org/10.1007/s11044-016-9530-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.32 ASE AR 39 2016 4 29 08 385-419 |
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10.1007/s11044-016-9530-y doi (DE-627)SPR016048539 (SPR)s11044-016-9530-y-e DE-627 ger DE-627 rakwb eng 600 ASE 50.32 bkl Marques, Filipe verfasserin aut On the constraints violation in forward dynamics of multibody systems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. Constraints violation (dpeaa)DE-He213 Baumgarte stabilization method (dpeaa)DE-He213 Penalty method (dpeaa)DE-He213 Augmented Lagrangian formulation (dpeaa)DE-He213 Index-1 Lagrangian formulation (dpeaa)DE-He213 Coordinate partitioning method (dpeaa)DE-He213 Mechanical energy (dpeaa)DE-He213 Computational efficiency (dpeaa)DE-He213 Forward dynamics (dpeaa)DE-He213 Multibody systems (dpeaa)DE-He213 Souto, António P. verfasserin aut Flores, Paulo verfasserin aut Enthalten in Multibody system dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 39(2016), 4 vom: 29. Aug., Seite 385-419 (DE-627)271181087 (DE-600)1479537-1 1573-272X nnns volume:39 year:2016 number:4 day:29 month:08 pages:385-419 https://dx.doi.org/10.1007/s11044-016-9530-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.32 ASE AR 39 2016 4 29 08 385-419 |
allfieldsGer |
10.1007/s11044-016-9530-y doi (DE-627)SPR016048539 (SPR)s11044-016-9530-y-e DE-627 ger DE-627 rakwb eng 600 ASE 50.32 bkl Marques, Filipe verfasserin aut On the constraints violation in forward dynamics of multibody systems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. Constraints violation (dpeaa)DE-He213 Baumgarte stabilization method (dpeaa)DE-He213 Penalty method (dpeaa)DE-He213 Augmented Lagrangian formulation (dpeaa)DE-He213 Index-1 Lagrangian formulation (dpeaa)DE-He213 Coordinate partitioning method (dpeaa)DE-He213 Mechanical energy (dpeaa)DE-He213 Computational efficiency (dpeaa)DE-He213 Forward dynamics (dpeaa)DE-He213 Multibody systems (dpeaa)DE-He213 Souto, António P. verfasserin aut Flores, Paulo verfasserin aut Enthalten in Multibody system dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 39(2016), 4 vom: 29. Aug., Seite 385-419 (DE-627)271181087 (DE-600)1479537-1 1573-272X nnns volume:39 year:2016 number:4 day:29 month:08 pages:385-419 https://dx.doi.org/10.1007/s11044-016-9530-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.32 ASE AR 39 2016 4 29 08 385-419 |
allfieldsSound |
10.1007/s11044-016-9530-y doi (DE-627)SPR016048539 (SPR)s11044-016-9530-y-e DE-627 ger DE-627 rakwb eng 600 ASE 50.32 bkl Marques, Filipe verfasserin aut On the constraints violation in forward dynamics of multibody systems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. Constraints violation (dpeaa)DE-He213 Baumgarte stabilization method (dpeaa)DE-He213 Penalty method (dpeaa)DE-He213 Augmented Lagrangian formulation (dpeaa)DE-He213 Index-1 Lagrangian formulation (dpeaa)DE-He213 Coordinate partitioning method (dpeaa)DE-He213 Mechanical energy (dpeaa)DE-He213 Computational efficiency (dpeaa)DE-He213 Forward dynamics (dpeaa)DE-He213 Multibody systems (dpeaa)DE-He213 Souto, António P. verfasserin aut Flores, Paulo verfasserin aut Enthalten in Multibody system dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 39(2016), 4 vom: 29. Aug., Seite 385-419 (DE-627)271181087 (DE-600)1479537-1 1573-272X nnns volume:39 year:2016 number:4 day:29 month:08 pages:385-419 https://dx.doi.org/10.1007/s11044-016-9530-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 50.32 ASE AR 39 2016 4 29 08 385-419 |
language |
English |
source |
Enthalten in Multibody system dynamics 39(2016), 4 vom: 29. Aug., Seite 385-419 volume:39 year:2016 number:4 day:29 month:08 pages:385-419 |
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Enthalten in Multibody system dynamics 39(2016), 4 vom: 29. Aug., Seite 385-419 volume:39 year:2016 number:4 day:29 month:08 pages:385-419 |
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topic_facet |
Constraints violation Baumgarte stabilization method Penalty method Augmented Lagrangian formulation Index-1 Lagrangian formulation Coordinate partitioning method Mechanical energy Computational efficiency Forward dynamics Multibody systems |
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Multibody system dynamics |
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Marques, Filipe @@aut@@ Souto, António P. @@aut@@ Flores, Paulo @@aut@@ |
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2016-08-29T00:00:00Z |
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This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constraints violation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Baumgarte stabilization method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Penalty method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Augmented Lagrangian formulation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Index-1 Lagrangian formulation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Coordinate partitioning method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mechanical energy</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational efficiency</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Forward dynamics</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multibody systems</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Souto, António P.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Flores, Paulo</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Multibody system dynamics</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997</subfield><subfield code="g">39(2016), 4 vom: 29. Aug., Seite 385-419</subfield><subfield code="w">(DE-627)271181087</subfield><subfield code="w">(DE-600)1479537-1</subfield><subfield code="x">1573-272X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:39</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:4</subfield><subfield code="g">day:29</subfield><subfield code="g">month:08</subfield><subfield code="g">pages:385-419</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s11044-016-9530-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" 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|
author |
Marques, Filipe |
spellingShingle |
Marques, Filipe ddc 600 bkl 50.32 misc Constraints violation misc Baumgarte stabilization method misc Penalty method misc Augmented Lagrangian formulation misc Index-1 Lagrangian formulation misc Coordinate partitioning method misc Mechanical energy misc Computational efficiency misc Forward dynamics misc Multibody systems On the constraints violation in forward dynamics of multibody systems |
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600 ASE 50.32 bkl On the constraints violation in forward dynamics of multibody systems Constraints violation (dpeaa)DE-He213 Baumgarte stabilization method (dpeaa)DE-He213 Penalty method (dpeaa)DE-He213 Augmented Lagrangian formulation (dpeaa)DE-He213 Index-1 Lagrangian formulation (dpeaa)DE-He213 Coordinate partitioning method (dpeaa)DE-He213 Mechanical energy (dpeaa)DE-He213 Computational efficiency (dpeaa)DE-He213 Forward dynamics (dpeaa)DE-He213 Multibody systems (dpeaa)DE-He213 |
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ddc 600 bkl 50.32 misc Constraints violation misc Baumgarte stabilization method misc Penalty method misc Augmented Lagrangian formulation misc Index-1 Lagrangian formulation misc Coordinate partitioning method misc Mechanical energy misc Computational efficiency misc Forward dynamics misc Multibody systems |
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ddc 600 bkl 50.32 misc Constraints violation misc Baumgarte stabilization method misc Penalty method misc Augmented Lagrangian formulation misc Index-1 Lagrangian formulation misc Coordinate partitioning method misc Mechanical energy misc Computational efficiency misc Forward dynamics misc Multibody systems |
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On the constraints violation in forward dynamics of multibody systems |
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On the constraints violation in forward dynamics of multibody systems |
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Marques, Filipe |
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Marques, Filipe Souto, António P. Flores, Paulo |
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10.1007/s11044-016-9530-y |
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title_sort |
on the constraints violation in forward dynamics of multibody systems |
title_auth |
On the constraints violation in forward dynamics of multibody systems |
abstract |
Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. |
abstractGer |
Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. |
abstract_unstemmed |
Abstract It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method. |
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container_issue |
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title_short |
On the constraints violation in forward dynamics of multibody systems |
url |
https://dx.doi.org/10.1007/s11044-016-9530-y |
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author2 |
Souto, António P. Flores, Paulo |
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up_date |
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|
score |
7.39966 |