de León, Manuel; Lainz, Manuel; López-Gordón, Asier; Marrero, Juan Carlos A new perspective on nonholonomic brackets and Hamilton-Jacobi theory. (English) Zbl 07812435 J. Geom. Phys. 198, Article ID 105116, 24 p. (2024). MSC: 37J60 70F25 70H20 53D17 53Z05 70G45 PDFBibTeX XMLCite \textit{M. de León} et al., J. Geom. Phys. 198, Article ID 105116, 24 p. (2024; Zbl 07812435) Full Text: DOI arXiv
De León, Manuel; Jiménez, Víctor M. The nonholonomic bracket on contact mechanical systems. arXiv:2312.15044 Preprint, arXiv:2312.15044 [math.DG] (2023). MSC: 37J55 53D10 37J60 70F25 70G45 53Z05 BibTeX Cite \textit{M. De León} and \textit{V. M. Jiménez}, ``The nonholonomic bracket on contact mechanical systems'', Preprint, arXiv:2312.15044 [math.DG] (2023) Full Text: arXiv OA License
de León, Manuel; Lainz, Manuel; López-Gordón, Asier Geometric Hamilton-Jacobi theory for systems with external forces. (English) Zbl 1507.70027 J. Math. Phys. 63, No. 2, Article ID 022901, 26 p. (2022). MSC: 70H20 35F21 70G45 70F25 37J60 70S05 PDFBibTeX XMLCite \textit{M. de León} et al., J. Math. Phys. 63, No. 2, Article ID 022901, 26 p. (2022; Zbl 1507.70027) Full Text: DOI arXiv
de León, Manuel; Jiménez, Víctor M.; Lainz, Manuel Contact Hamiltonian and Lagrangian systems with nonholonomic constraints. (English) Zbl 1496.37071 J. Geom. Mech. 13, No. 1, 25-53 (2021). Reviewer: Alfonso Giuseppe Tortorella (Porto) MSC: 37J60 37J55 70F25 53D10 70H33 PDFBibTeX XMLCite \textit{M. de León} et al., J. Geom. Mech. 13, No. 1, 25--53 (2021; Zbl 1496.37071) Full Text: DOI arXiv
de León, Manuel; Martín de Diego, David; Vaquero, Miguel A Hamilton-Jacobi theory on Poisson manifolds. (English) Zbl 1304.70019 J. Geom. Mech. 6, No. 1, 121-140 (2014). MSC: 70H20 70F25 37J60 PDFBibTeX XMLCite \textit{M. de León} et al., J. Geom. Mech. 6, No. 1, 121--140 (2014; Zbl 1304.70019) Full Text: DOI
De León, Manuel A historical review on nonholomic mechanics. (English) Zbl 1264.37017 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 106, No. 1, 191-224 (2012). Reviewer: Bojidar Cheshankov (Sofia) MSC: 37J60 70F25 70H20 70H33 PDFBibTeX XMLCite \textit{M. De León}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 106, No. 1, 191--224 (2012; Zbl 1264.37017) Full Text: DOI
de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. (English) Zbl 1226.37045 J. Geom. Mech. 2, No. 2, 159-198 (2010). Reviewer: Liviu Popescu (Craiova) MSC: 37J60 53D17 70F25 70G45 70H20 PDFBibTeX XMLCite \textit{M. de León} et al., J. Geom. Mech. 2, No. 2, 159--198 (2010; Zbl 1226.37045) Full Text: DOI arXiv
Grabowski, Janusz; de León, Manuel; Marrero, J. C.; Martín de Diego, D. Nonholonomic constraints: a new viewpoint. (English) Zbl 1200.37057 J. Math. Phys. 50, No. 1, 013520, 17 p. (2009). MSC: 37J60 53D99 70F25 70G45 70H03 PDFBibTeX XMLCite \textit{J. Grabowski} et al., J. Math. Phys. 50, No. 1, 013520, 17 p. (2009; Zbl 1200.37057) Full Text: DOI arXiv
Cortés, Jorge; de León, Manuel; Marrero, Juan Carlos; Martínez, Eduardo Nonholonomic Lagrangian systems on Lie algebroids. (English) Zbl 1161.70336 Discrete Contin. Dyn. Syst. 24, No. 2, 213-271 (2009). MSC: 70F25 70H03 70H33 37J60 53D17 PDFBibTeX XMLCite \textit{J. Cortés} et al., Discrete Contin. Dyn. Syst. 24, No. 2, 213--271 (2009; Zbl 1161.70336) Full Text: DOI
Iglesias-Ponte, David; de León, Manuel; Martín de Diego, David Towards a Hamilton-Jacobi theory for nonholonomic mechanical systems. (English) Zbl 1154.70007 J. Phys. A, Math. Theor. 41, No. 1, Article ID 015205, 14 p. (2008). MSC: 70H20 70F25 37J60 37M15 PDFBibTeX XMLCite \textit{D. Iglesias-Ponte} et al., J. Phys. A, Math. Theor. 41, No. 1, Article ID 015205, 14 p. (2008; Zbl 1154.70007) Full Text: DOI arXiv
Cortés, Jorge; De León, Manuel; Marrero, Juan C.; Martín De Diego, D.; Martínez, Eduardo A survey of Lagrangian mechanics and control on Lie algebroids and groupoids. (English) Zbl 1136.70317 Int. J. Geom. Methods Mod. Phys. 3, No. 3, 509-558 (2006). MSC: 70G45 37J05 58E30 70H03 70Q05 17B66 22A22 70F25 PDFBibTeX XMLCite \textit{J. Cortés} et al., Int. J. Geom. Methods Mod. Phys. 3, No. 3, 509--558 (2006; Zbl 1136.70317) Full Text: DOI arXiv
Cortes, J.; de Leon, M.; Marrero, J. C.; Martinez, E. Non-holonomic Lagrangian systems on Lie algebroids. arXiv:math-ph/0512003 Preprint, arXiv:math-ph/0512003 [math-ph] (2005). MSC: 70F25 70H03 70H33 37J60 53D17 BibTeX Cite \textit{J. Cortes} et al., ``Non-holonomic Lagrangian systems on Lie algebroids'', Preprint, arXiv:math-ph/0512003 [math-ph] (2005) Full Text: arXiv
de León, M.; Martín de Diego, D.; Santamaría-Merino, A. Geometric integrators and nonholonomic mechanics. (English) Zbl 1070.37058 J. Math. Phys. 45, No. 3, 1042-1064 (2004). MSC: 37M15 37J60 65P10 70-08 70F25 PDFBibTeX XMLCite \textit{M. de León} et al., J. Math. Phys. 45, No. 3, 1042--1064 (2004; Zbl 1070.37058) Full Text: DOI arXiv
de León, Manuel; Cortés, Jorge; Martín de Diego, David; Martínez, Sonia General symmetries in optimal control. (English) Zbl 1085.49028 Rep. Math. Phys. 53, No. 1, 55-78 (2004). MSC: 49K15 37J15 37J60 70F25 93C15 PDFBibTeX XMLCite \textit{M. de León} et al., Rep. Math. Phys. 53, No. 1, 55--78 (2004; Zbl 1085.49028) Full Text: DOI
Binz, Ernst; de León, Manuel; Martín de Diego, David; Socolescu, Dan Nonholonomic constraints in classical field theories. (English) Zbl 1024.70015 Rep. Math. Phys. 49, No. 2-3, 151-166 (2002). Reviewer: Jürgen Tolksdorf (Mannheim) MSC: 70S05 70F25 70G45 37J60 PDFBibTeX XMLCite \textit{E. Binz} et al., Rep. Math. Phys. 49, No. 2--3, 151--166 (2002; Zbl 1024.70015) Full Text: DOI arXiv
Cortés, Jorge; de León, Manuel; Martín de Diego, David; Martínez, Sonia Non-constant rank constraints. (English) Zbl 1142.70317 del Olmo Martínez, Mariano A. (ed.) et al., Actas del octavo encuentro de otoño de geometría y física. Madrid: Real Sociedad Matemática Española (ISBN 84-923818-4-1/pbk). Publ. R. Soc. Mat. Esp. 2, 41-54 (2001). MSC: 70F25 70H45 37J60 53D05 70G45 PDFBibTeX XMLCite \textit{J. Cortés} et al., Publ. R. Soc. Mat. Esp. 2, 41--54 (2001; Zbl 1142.70317)
Ibort, Alberto; de León, Manuel; Lacomba, Ernesto A.; Marrero, Juan C.; Martín de Diego, David Geometric formulation of Carnot’s theorem. (English) Zbl 1050.70010 J. Phys. A, Math. Gen. 34, No. 8, 1691-1712 (2001). MSC: 70G45 37J60 70F25 70F40 70H03 PDFBibTeX XMLCite \textit{A. Ibort} et al., J. Phys. A, Math. Gen. 34, No. 8, 1691--1712 (2001; Zbl 1050.70010) Full Text: DOI
de León, Manuel; Marrero, Juan C.; Martín de Diego, David The geometry of the phase space of a nonholonomic mechanical system. (English) Zbl 0984.53033 Llinares Fuster, Elisa (ed.) et al., Proceedings of the 7th fall workshop on differential geometry and its applications, Valencia, Spain, September 21-23, 1998. Madrid: Real Sociedad Matemática Española. Publ. R. Soc. Mat. Esp. 1, 107-118 (2000). Reviewer: Paulo R.Rodrigues (Rio de Janeiro) MSC: 53D12 70F25 53D05 37J05 PDFBibTeX XMLCite \textit{M. de León} et al., Publ. R. Soc. Mat. Esp. 1, 107--118 (2000; Zbl 0984.53033)
Cantrijn, F.; de León, M.; Marrero, Juan Carlos; Martín de Diego, D. On almost-Poisson structures in nonholonomic mechanics. II: The time-dependent framework. (English) Zbl 0963.37054 Nonlinearity 13, No. 4, 1379-1409 (2000). Reviewer: Messoud Efendiev (Berlin) MSC: 37J60 70H45 53D17 70F25 70H05 PDFBibTeX XMLCite \textit{F. Cantrijn} et al., Nonlinearity 13, No. 4, 1379--1409 (2000; Zbl 0963.37054) Full Text: DOI
Cantrijn, F.; de León, M.; Martín de Diego, D. On almost-Poisson structures in nonholonomic mechanics. (English) Zbl 0984.37076 Nonlinearity 12, No. 3, 721-737 (1999). MSC: 37J60 53D17 70F25 70H05 70H45 PDFBibTeX XMLCite \textit{F. Cantrijn} et al., Nonlinearity 12, No. 3, 721--737 (1999; Zbl 0984.37076) Full Text: DOI
Ibort, Alberto; de Leon, Manuel; Marrero, Juan C.; Martin de Diego, David Dirac brackets in constrained dynamics. (English) Zbl 0956.37049 Fortschr. Phys. 47, No. 5, 459-492 (1999). MSC: 37J60 53D17 70F25 70H03 70H45 PDFBibTeX XMLCite \textit{A. Ibort} et al., Fortschr. Phys. 47, No. 5, 459--492 (1999; Zbl 0956.37049) Full Text: DOI
Cortés, Jorge; de León, Manuel Reduction and reconstruction of the dynamics of nonholonomic systems. (English) Zbl 0965.70023 J. Phys. A, Math. Gen. 32, No. 49, 8615-8645 (1999). Reviewer: Samir Musayev (Baku) MSC: 70F25 70H33 37N05 37J60 37J15 PDFBibTeX XMLCite \textit{J. Cortés} and \textit{M. de León}, J. Phys. A, Math. Gen. 32, No. 49, 8615--8645 (1999; Zbl 0965.70023) Full Text: DOI Link
Cantrijn, Frans; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David Reduction of constrained systems with symmetries. (English) Zbl 0974.37050 J. Math. Phys. 40, No. 2, 795-820 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37J60 70H05 37J15 70F25 70H33 PDFBibTeX XMLCite \textit{F. Cantrijn} et al., J. Math. Phys. 40, No. 2, 795--820 (1999; Zbl 0974.37050) Full Text: DOI Link
Ibort, Alberto; de León, Manuel; Marrero, Juan C.; Martín de Diego, David A Dirac bracket for non-holonomic Lagrangian systems. (English) Zbl 0934.37052 Cariñena, J. F. (ed.) et al., Geometry and physics. Proceedings of the 5th fall workshop, Jaca, Spain, September 23-25, 1996. Madrid: Real Academia de Ciencias Exactas, Físicas y Naturales. Mem. R. Acad. Cienc. Exactas Fis. Nat. Madrid, Ser. Cienc. Exactas. 32, 85-101 (1998). Reviewer: Roland Wisk (Berlin) MSC: 37J60 37N05 70F25 70H45 37K05 PDFBibTeX XMLCite \textit{A. Ibort} et al., in: Geometría y física. Actas de la reunión de otoño, Jaca, España, 1996. Madrid: Real Academia de Ciencias Exactas, Físicas y Naturales. 85--101 (1998; Zbl 0934.37052)
Cantrijn, Frans; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David Reduction of nonholonomic mechanical systems with symmetries. (English) Zbl 0973.37505 Rep. Math. Phys. 42, No. 1-2, 25-45 (1998). MSC: 37K30 53D20 70H33 37J15 70H45 70F25 PDFBibTeX XMLCite \textit{F. Cantrijn} et al., Rep. Math. Phys. 42, No. 1--2, 25--45 (1998; Zbl 0973.37505) Full Text: DOI
de León, Manuel; Marrero, Juan C.; Martín de Diego, David Non-holonomic Lagrangian systems in jet manifolds. (English) Zbl 1001.70505 J. Phys. A, Math. Gen. 30, No. 4, 1167-1190 (1997). MSC: 70F25 37Jxx 70H03 PDFBibTeX XMLCite \textit{M. de León} et al., J. Phys. A, Math. Gen. 30, No. 4, 1167--1190 (1997; Zbl 1001.70505) Full Text: DOI
de León, Manuel; Martín de Diego, David A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints. (English) Zbl 0878.58027 J. Math. Phys. 38, No. 6, 3055-3062 (1997). MSC: 37J60 70F25 70H03 70H45 PDFBibTeX XMLCite \textit{M. de León} and \textit{D. Martín de Diego}, J. Math. Phys. 38, No. 6, 3055--3062 (1997; Zbl 0878.58027) Full Text: DOI Link
de León, Manuel; Marrero, Juan C.; Martín de Diego, David Mechanical systems with nonlinear constraints. (English) Zbl 0874.70012 Int. J. Theor. Phys. 36, No. 4, 979-995 (1997). MSC: 70F25 70H03 37J60 53C15 PDFBibTeX XMLCite \textit{M. de León} et al., Int. J. Theor. Phys. 36, No. 4, 979--995 (1997; Zbl 0874.70012) Full Text: DOI
de León, Manuel; Martín de Diego, David On the geometry of non-holonomic Lagrangian systems. (English) Zbl 0869.70008 J. Math. Phys. 37, No. 7, 3389-3414 (1996). MSC: 70F25 37J60 70H03 70G10 70H45 PDFBibTeX XMLCite \textit{M. de León} and \textit{D. Martín de Diego}, J. Math. Phys. 37, No. 7, 3389--3414 (1996; Zbl 0869.70008) Full Text: DOI
de León, Manuel; Martín de Diego, David A symplectic formulation of non-holonomic Lagrangian systems. (English) Zbl 0934.37053 Salgado, Modesto (ed.) et al., WOGDA ’95. Proceedings of the 4th fall workshop on differential geometry and its applications, Santiago de Compostela, Spain, September 18-20, 1995. Madrid: CIEMAT. An. Fís., Monogr. 3, 125-137 (1996). Reviewer: Roland Wisk (Berlin) MSC: 37J60 70F25 70F45 37J10 70H03 PDFBibTeX XMLCite \textit{M. de León} and \textit{D. Martín de Diego}, An. Fís., Monogr. 3, 125--137 (1996; Zbl 0934.37053)
Ibort, Alberto; de León, Manuel; Marmo, G.; Martín de Diego, David Non-holonomic constrained systems as implicit differential equations. (English) Zbl 0928.70031 Rend. Semin. Mat., Torino 54, No. 3, 295-317 (1996). MSC: 70F25 70G45 37J60 PDFBibTeX XMLCite \textit{A. Ibort} et al., Rend. Semin. Mat., Torino 54, No. 3, 295--317 (1996; Zbl 0928.70031) Full Text: arXiv
de Léon, Manuel; Martín de Diego, David Solving non-holonomic Lagrangian dynamics in terms of almost product structures. (English) Zbl 0892.58028 Extr. Math. 11, No. 2, 325-347 (1996). Reviewer: Y.Kozai (Tokyo) MSC: 37J60 70F25 53C15 70H03 PDFBibTeX XMLCite \textit{M. de Léon} and \textit{D. Martín de Diego}, Extr. Math. 11, No. 2, 325--347 (1996; Zbl 0892.58028) Full Text: EuDML
de León, Manuel; LaComba, Ernesto A. Les sous-variétés lagrangiennes dans la dynamique lagrangienne d’ordre supérieur. (Lagrangian submanifolds and higher-order Lagrangian dynamics). (French. English summary) Zbl 0646.70015 C. R. Acad. Sci., Paris, Sér. II 307, No. 10, 1137-1139 (1988). MSC: 70H03 37J99 PDFBibTeX XMLCite \textit{M. de León} and \textit{E. A. LaComba}, C. R. Acad. Sci., Paris, Sér. II 307, No. 10, 1137--1139 (1988; Zbl 0646.70015)
de Leon, Manuel Transformation de Legendre pour les systèmes lagrangiens réguliers d’ordre supérieur. (French) Zbl 0501.58021 C. R. Acad. Sci., Paris, Sér. I 295, 123-125 (1982). MSC: 37J99 58A17 53B50 PDFBibTeX XMLCite \textit{M. de Leon}, C. R. Acad. Sci., Paris, Sér. I 295, 123--125 (1982; Zbl 0501.58021) Full Text: EuDML