Gao, Shan; Shi, Donghua; Zenkov, Dmitry V. Discrete Hamiltonian variational mechanics and Hamel’s integrators. (English) Zbl 1513.70050 J. Nonlinear Sci. 33, No. 2, Paper No. 26, 58 p. (2023); correction ibid. 33, No. 2, Paper No. 36, 1 p. (2023). MSC: 70F25 37J60 70H33 PDFBibTeX XMLCite \textit{S. Gao} et al., J. Nonlinear Sci. 33, No. 2, Paper No. 26, 58 p. (2023; Zbl 1513.70050) Full Text: DOI
Chen, Xin; Cruzeiro, Ana Bela; Ratiu, Tudor S. Stochastic variational principles for dissipative equations with advected quantities. (English) Zbl 1524.76329 J. Nonlinear Sci. 33, No. 1, Paper No. 5, 62 p. (2023). MSC: 76M60 76W05 76E25 76M35 76M30 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Nonlinear Sci. 33, No. 1, Paper No. 5, 62 p. (2023; Zbl 1524.76329) Full Text: DOI arXiv
Kong, Xinlei; Wang, Zhongxin; Wu, Huibin Variational integrators for forced Lagrangian systems based on the local path fitting technique. (English) Zbl 1510.70041 Appl. Math. Comput. 416, Article ID 126739, 20 p. (2022). MSC: 70G75 65P10 PDFBibTeX XMLCite \textit{X. Kong} et al., Appl. Math. Comput. 416, Article ID 126739, 20 p. (2022; Zbl 1510.70041) Full Text: DOI
García-Naranjo, Luis C.; Vermeeren, Mats Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics. (English) Zbl 1479.37082 J. Comput. Dyn. 8, No. 3, 241-271 (2021). MSC: 37M15 65P10 37J60 70G45 PDFBibTeX XMLCite \textit{L. C. García-Naranjo} and \textit{M. Vermeeren}, J. Comput. Dyn. 8, No. 3, 241--271 (2021; Zbl 1479.37082) Full Text: DOI arXiv
Modin, Klas; Verdier, Olivier What makes nonholonomic integrators work? (English) Zbl 1447.37068 Numer. Math. 145, No. 2, 405-435 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 37M15 65P10 37J60 37J40 70F25 37N30 65D30 37J35 PDFBibTeX XMLCite \textit{K. Modin} and \textit{O. Verdier}, Numer. Math. 145, No. 2, 405--435 (2020; Zbl 1447.37068) Full Text: DOI arXiv
An, Zhipeng; Gao, Shan; Shi, Donghua; Zenkov, Dmitry V. A variational integrator for the Chaplygin-Timoshenko sleigh. (English) Zbl 1447.70018 J. Nonlinear Sci. 30, No. 4, 1381-1419 (2020). MSC: 70F25 37J60 70H33 70S05 PDFBibTeX XMLCite \textit{Z. An} et al., J. Nonlinear Sci. 30, No. 4, 1381--1419 (2020; Zbl 1447.70018) Full Text: DOI
Sharma, Harsh; Patil, Mayuresh; Woolsey, Craig A review of structure-preserving numerical methods for engineering applications. (English) Zbl 1442.65444 Comput. Methods Appl. Mech. Eng. 366, Article ID 113067, 22 p. (2020). MSC: 65P10 70-08 74Sxx PDFBibTeX XMLCite \textit{H. Sharma} et al., Comput. Methods Appl. Mech. Eng. 366, Article ID 113067, 22 p. (2020; Zbl 1442.65444) Full Text: DOI
Glaas, Daniel; Leyendecker, Sigrid Variational integrator based optimal feedback control for constrained mechanical systems. (English) Zbl 07804228 ZAMM, Z. Angew. Math. Mech. 99, No. 1, Article ID e201700221, 20 p. (2019). MSC: 65Pxx 37Jxx 65Lxx PDFBibTeX XMLCite \textit{D. Glaas} and \textit{S. Leyendecker}, ZAMM, Z. Angew. Math. Mech. 99, No. 1, Article ID e201700221, 20 p. (2019; Zbl 07804228) Full Text: DOI
Chang, Dong Eui; Perlmutter, Matthew Feedback integrators for nonholonomic mechanical systems. (English) Zbl 1483.65202 J. Nonlinear Sci. 29, No. 3, 1165-1204 (2019). MSC: 65P10 37M15 70E15 70F25 93D15 PDFBibTeX XMLCite \textit{D. E. Chang} and \textit{M. Perlmutter}, J. Nonlinear Sci. 29, No. 3, 1165--1204 (2019; Zbl 1483.65202) Full Text: DOI arXiv
Mergel, Janine C.; Sauer, Roger A.; Ober-Blöbaum, Sina \(C^1\)-continuous space-time discretization based on Hamilton’s law of varying action. (English) Zbl 07775183 ZAMM, Z. Angew. Math. Mech. 97, No. 4, 433-457 (2017). MSC: 37M15 65P10 70H25 74B20 74H15 74S05 PDFBibTeX XMLCite \textit{J. C. Mergel} et al., ZAMM, Z. Angew. Math. Mech. 97, No. 4, 433--457 (2017; Zbl 07775183) Full Text: DOI arXiv
Hall, James; Leok, Melvin Lie group spectral variational integrators. (English) Zbl 1377.37115 Found. Comput. Math. 17, No. 1, 199-257 (2017). Reviewer: Kai Schneider (Marseille) MSC: 37M15 65M70 65P10 70G75 70H25 PDFBibTeX XMLCite \textit{J. Hall} and \textit{M. Leok}, Found. Comput. Math. 17, No. 1, 199--257 (2017; Zbl 1377.37115) Full Text: DOI arXiv
Zenkov, Dmitry V. On Hamel’s equations. (English) Zbl 1474.70024 Theor. Appl. Mech. (Belgrade) 43, No. 2, 191-220 (2016). MSC: 70H30 70F25 37J60 74F99 PDFBibTeX XMLCite \textit{D. V. Zenkov}, Theor. Appl. Mech. (Belgrade) 43, No. 2, 191--220 (2016; Zbl 1474.70024) Full Text: DOI
Fu, Minghui; Lu, Kelang; Li, Weihua; Sheshenin, S. V. New way to construct high order Hamiltonian variational integrators. (English) Zbl 1348.70049 AMM, Appl. Math. Mech., Engl. Ed. 37, No. 8, 1041-1052 (2016). MSC: 70H25 65P10 35A24 PDFBibTeX XMLCite \textit{M. Fu} et al., AMM, Appl. Math. Mech., Engl. Ed. 37, No. 8, 1041--1052 (2016; Zbl 1348.70049) Full Text: DOI
Cai, Wenjun; Sun, Yajuan; Wang, Yushun Variational discretizations for the generalized Rosenau-type equations. (English) Zbl 1410.65302 Appl. Math. Comput. 271, 860-873 (2015). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{W. Cai} et al., Appl. Math. Comput. 271, 860--873 (2015; Zbl 1410.65302) Full Text: DOI
Ober-Blöbaum, Sina; Saake, Nils Construction and analysis of higher order Galerkin variational integrators. (English) Zbl 1337.37063 Adv. Comput. Math. 41, No. 6, 955-986 (2015). MSC: 37M15 37J45 70H25 65L60 70H03 39A12 PDFBibTeX XMLCite \textit{S. Ober-Blöbaum} and \textit{N. Saake}, Adv. Comput. Math. 41, No. 6, 955--986 (2015; Zbl 1337.37063) Full Text: DOI arXiv
Campos, Cédric M.; Ober-Blöbaum, Sina; Trélat, Emmanuel High order variational integrators in the optimal control of mechanical systems. (English) Zbl 1332.65184 Discrete Contin. Dyn. Syst. 35, No. 9, 4193-4223 (2015). MSC: 65P10 65L06 65K10 49Mxx PDFBibTeX XMLCite \textit{C. M. Campos} et al., Discrete Contin. Dyn. Syst. 35, No. 9, 4193--4223 (2015; Zbl 1332.65184) Full Text: DOI arXiv
Ball, Kenneth R.; Zenkov, Dmitry V. Hamel’s formalism and variational integrators. (English) Zbl 1367.70061 Chang, Dong Eui (ed.) et al., Geometry, mechanics, and dynamics. The legacy of Jerry Marsden. Selected papers presented at a focus program, Fields Institute for Research in Mathematical Sciences, Toronto, Canada, July 2012. New York, NY: Springer (ISBN 978-1-4939-2440-0/hbk; 978-1-4939-2441-7/ebook). Fields Institute Communications 73, 477-506 (2015). MSC: 70S05 37J05 65P99 PDFBibTeX XMLCite \textit{K. R. Ball} and \textit{D. V. Zenkov}, Fields Inst. Commun. 73, 477--506 (2015; Zbl 1367.70061) Full Text: DOI
Campos, Cédric M. High order variational integrators: a polynomial approach. (English) Zbl 1326.65173 Casas, Fernando (ed.) et al., Advances in differential equations and applications. Selected contributions given at the 23rd congress on differential equations and applications, CEDYA/13th congress of applied mathematics, CMA, September 9–13, 2013. Cham: Springer (ISBN 978-3-319-06952-4/hbk; 978-3-319-06953-1/ebook). SEMA SIMAI Springer Series 4, 249-258 (2015). MSC: 65P10 65L06 37M15 65K10 49J15 PDFBibTeX XMLCite \textit{C. M. Campos}, SEMA SIMAI Springer Ser. 4, 249--258 (2015; Zbl 1326.65173) Full Text: DOI arXiv
Natsiavas, S.; Paraskevopoulos, E. A set of ordinary differential equations of motion for constrained mechanical systems. (English) Zbl 1331.70056 Nonlinear Dyn. 79, No. 3, 1911-1938 (2015). MSC: 70H45 70F20 70F25 70G45 37N05 PDFBibTeX XMLCite \textit{S. Natsiavas} and \textit{E. Paraskevopoulos}, Nonlinear Dyn. 79, No. 3, 1911--1938 (2015; Zbl 1331.70056) Full Text: DOI
Demoures, F.; Gay-Balmaz, F.; Leyendecker, S.; Ober-Blöbaum, S.; Ratiu, T. S.; Weinand, Y. Discrete variational Lie group formulation of geometrically exact beam dynamics. (English) Zbl 1315.53090 Numer. Math. 130, No. 1, 73-123 (2015). MSC: 53D05 65P10 74B20 74H15 37M15 PDFBibTeX XMLCite \textit{F. Demoures} et al., Numer. Math. 130, No. 1, 73--123 (2015; Zbl 1315.53090) Full Text: DOI HAL
Modin, Klas; Verdier, Olivier Integrability of nonholonomically coupled oscillators. (English) Zbl 1368.70023 Discrete Contin. Dyn. Syst. 34, No. 3, 1121-1130 (2014). MSC: 70F25 37J60 37M15 65P99 70H08 PDFBibTeX XMLCite \textit{K. Modin} and \textit{O. Verdier}, Discrete Contin. Dyn. Syst. 34, No. 3, 1121--1130 (2014; Zbl 1368.70023) Full Text: DOI arXiv
Ober-Blöbaum, Sina; Tao, Molei; Cheng, Mulin; Owhadi, Houman; Marsden, Jerrold E. Variational integrators for electric circuits. (English) Zbl 1298.78024 J. Comput. Phys. 242, 498-530 (2013). MSC: 78A55 94C05 78M30 PDFBibTeX XMLCite \textit{S. Ober-Blöbaum} et al., J. Comput. Phys. 242, 498--530 (2013; Zbl 1298.78024) Full Text: DOI arXiv Link
Leyendecker, Sigrid; Ober-Blöbaum, Sina A variational approach to multirate integration for constrained systems. (English) Zbl 1311.70026 Samin, Jean-Claude et al., Multibody dynamics. Computational methods and applications. Selected papers based on the presentations at the ECCOMAS thematic conference, Brussels, Belgium, July 4–7, 2011. Dordrecht: Springer (ISBN 978-94-007-5403-4/hbk; 978-94-007-5404-1/ebook). Computational Methods in Applied Sciences (Springer) 28, 97-121 (2013). MSC: 70H03 49M25 65P10 70G75 70H45 PDFBibTeX XMLCite \textit{S. Leyendecker} and \textit{S. Ober-Blöbaum}, in: Multibody dynamics. Computational methods and applications. Selected papers based on the presentations at the ECCOMAS thematic conference, Brussels, Belgium, July 4--7, 2011. Dordrecht: Springer. 97--121 (2013; Zbl 1311.70026) Full Text: DOI
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David Discrete variational optimal control. (English) Zbl 1319.70031 J. Nonlinear Sci. 23, No. 3, 393-426 (2013). MSC: 70Q05 49M30 37M15 70H03 37J60 PDFBibTeX XMLCite \textit{F. Jiménez} et al., J. Nonlinear Sci. 23, No. 3, 393--426 (2013; Zbl 1319.70031) Full Text: DOI arXiv
Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin Solving optimal control problems by exploiting inherent dynamical systems structures. (English) Zbl 1264.37013 J. Nonlinear Sci. 22, No. 4, 599-629 (2012). Reviewer: Bojidar Cheshankov (Sofia) MSC: 37J15 49M37 70Q05 PDFBibTeX XMLCite \textit{K. Flaßkamp} et al., J. Nonlinear Sci. 22, No. 4, 599--629 (2012; Zbl 1264.37013) Full Text: DOI