# zbMATH — the first resource for mathematics

## Journal of Geometric Mechanics

 Short Title: J. Geom. Mech. Publisher: American Institute of Mathematical Sciences (AIMS), Springfield, MO ISSN: 1941-4889; 1941-4897/e Online: http://aimsciences.org/journals/home.jsp?journalID=17 Comments: Indexed cover-to-cover
 Documents Indexed: 261 Publications (since 2009) References Indexed: 145 Publications with 4,511 References.
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#### Latest Issues

 13, No. 2 (2021) 12, No. 3 (2020) 12, No. 2 (2020) 12, No. 1 (2020) 11, No. 4 (2019) 11, No. 3 (2019) 11, No. 2 (2019) 11, No. 1 (2019) 10, No. 4 (2018) 10, No. 3 (2018) 10, No. 2 (2018) 10, No. 1 (2018) 9, No. 4 (2017) 9, No. 3 (2017) 9, No. 2 (2017) 9, No. 1 (2017) 8, No. 4 (2016) 8, No. 3 (2016) 8, No. 2 (2016) 8, No. 1 (2016) 7, No. 4 (2015) 7, No. 3 (2015) 7, No. 2 (2015) 7, No. 1 (2015) 6, No. 4 (2014) 6, No. 3 (2014) 6, No. 2 (2014) 6, No. 1 (2014) 5, No. 4 (2013) 5, No. 3 (2013) 5, No. 2 (2013) 5, No. 1 (2013) 4, No. 4 (2012) 4, No. 3 (2012) 4, No. 2 (2012) 4, No. 1 (2012) 3, No. 4 (2011) 3, No. 3 (2011) 3, No. 2 (2011) 3, No. 1 (2011) 2, No. 4 (2010) 2, No. 3 (2010) 2, No. 2 (2010) 2, No. 1 (2010) 1, No. 4 (2009) 1, No. 3 (2009) 1, No. 2 (2009) 1, No. 1 (2009)
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#### Authors

 9 Martín de Diego, David 8 de León Rodríguez, Manuel 8 Román-Roy, Narciso 7 Grabowska, Katarzyna 6 Castrillón López, Marco 6 Ferrer, Sebastián 6 Tronci, Cesare 5 Bloch, Anthony M. 5 Fassò, Francesco 5 Gay-Balmaz, François 5 Holm, Darryl D. 5 Marrero, Juan Carlos 5 Ortega, Juan-Pablo 5 Zuccalli, Marcela 4 Cendra, Hernán 4 Crespo, Francisco 4 Esen, Oğul 4 Fernandez, Javier Alejandro 4 García, Pedro Luis 4 Grillo, Sergio Daniel 4 Michor, Peter Wolfram 4 Montaldi, James A. 4 Ratiu, Tudor Stefan 4 Sansonetto, Nicola 4 Scheurle, Jürgen 3 Bauer, Martin 3 Bruveris, Martins 3 Colombo, Leonardo Jesus 3 Crampin, Mike 3 Dullin, Holger R. 3 Escher, Joachim 3 Fernández Martínez, Antonio 3 García-Naranjo, Luis C. 3 Grabowski, Janusz 3 Jóźwikowski, Michał 3 Koiller, Jair 3 Kolev, Boris 3 Kupferman, Raz 3 Lewis, Andrew D. 3 Marsden, Jerrold Eldon 3 Muñoz-Lecanda, Miguel C. 3 Urbański, Paweł 3 Vizman, Cornelia 2 Balseiro, Paula 2 Barbero-Liñán, María 2 Bates, Larry M. 2 Bucataru, Ioan 2 Cabrera, Alejandro 2 Cariñena, José F. 2 Cotter, Colin John 2 Crouch, Peter E. 2 Cruz, Inês 2 Díaz, Viviana Alejandra 2 Durán Fernandez, Carlos Eduardo 2 Ferraro, Sebastián J. 2 Giacobbe, Andrea 2 Gràcia, Xavier 2 Harms, Philipp 2 Hohloch, Sonja 2 Hone, Andrew N. W. 2 Ibort, Alberto 2 Ivanov, Rossen I. 2 Jacobs, Henry O. 2 Jiménez, Fernando 2 Mestdag, Tom 2 Molero, Francisco Javier 2 Nordkvist, Nikolaj 2 Ohsawa, Tomoki 2 Olver, Peter John 2 Otero, Diego 2 Poncin, Norbert 2 Prieto-Martínez, Pedro Daniel 2 Rañada, Manuel F. 2 Respondek, Witold 2 Rivas, Xavier 2 Rodrigo, César 2 Rotkiewicz, Mikołaj 2 Salgado, Modesto R. 2 Shachar, Asaf 2 Shaddad, Amna 2 Shafiee, Mohammad Ali 2 Shanbrom, Corey 2 Shashikanth, Banavara N. 2 Śniatycki, Jędrzej 2 Stoica, Cristina 2 Thompson, Gerard 2 Tori, Cora 2 Tsyganov, Andreĭ Vladimirovich 2 Van Goethem, Nicolas 2 Vankerschaver, Joris 2 Vorobiev, Yurii 2 Walcher, Sebastian 2 Yoshimura, Hiroaki 2 Zambrini, Jean-Claude 1 Albeverio, Sergio A. 1 Albouy, Alain 1 Alishah, Hassan Najafi 1 Amrane, Yacine Aït 1 Antunes, Paulo 1 Arnaudon, Alexis ...and 242 more Authors
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#### Fields

 135 Mechanics of particles and systems (70-XX) 124 Differential geometry (53-XX) 112 Dynamical systems and ergodic theory (37-XX) 52 Global analysis, analysis on manifolds (58-XX) 33 Partial differential equations (35-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 24 Ordinary differential equations (34-XX) 18 Fluid mechanics (76-XX) 17 Topological groups, Lie groups (22-XX) 15 Numerical analysis (65-XX) 11 Mechanics of deformable solids (74-XX) 10 Nonassociative rings and algebras (17-XX) 10 Systems theory; control (93-XX) 9 Probability theory and stochastic processes (60-XX) 7 Quantum theory (81-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 General and overarching topics; collections (00-XX) 6 Manifolds and cell complexes (57-XX) 5 History and biography (01-XX) 4 Algebraic geometry (14-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Functional analysis (46-XX) 3 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 3 Statistics (62-XX) 3 Relativity and gravitational theory (83-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Algebraic topology (55-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

181 Publications have been cited 902 times in 655 Documents Cited by Year
Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Zbl 1226.37045
de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David
2010
Sobolev metrics on shape space of surfaces. Zbl 1262.58004
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2011
Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle. Zbl 1308.58005
Escher, Joachim; Kolev, Boris
2014
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
2013
Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms. Zbl 1330.37057
Suris, Yuri B.
2013
Integrable Euler top and nonholonomic Chaplygin ball. Zbl 1348.70014
Tsiganov, Andrey
2011
Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics. Zbl 1281.58003
Bauer, Martin; Harms, Philipp; Michor, Peter W.
2012
$$G$$-Chaplygin systemswith internal symmetries, truncation, and an (almost) symplecticview of Chaplygin’s ball. Zbl 1168.53327
Hochgerner, Simon; García-Naranjo, Luis
2009
Clebsch optimal control formulation in mechanics. Zbl 1233.49005
Gay-Balmaz, François; Ratiu, Tudor S.
2011
Geodesic Vlasov equations and their integrable moment closures. Zbl 1190.82033
Holm, Darryl D.; Tronci, Cesare
2009
Nonholonomic Hamilton-Jacobi equation and integrability. Zbl 1288.70009
Ohsawa, Tomoki; Bloch, Anthony M.
2009
The supergeometry of Loday algebroids. Zbl 1294.53072
Grabowski, Janusz; Khudaverdyan, David; Poncin, Norbert
2013
Higher-order variational problems on Lie groups and optimal control applications. Zbl 1307.70018
Colombo, Leonardo; Martín de Diego, David
2014
Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras. Zbl 1168.37318
Hone, Andrew N. W.; Petrera, Matteo
2009
Point vortices on the sphere: stability of symmetric relative equilibria. Zbl 1248.70020
Laurent-Polz, Frederic; Montaldi, James; Roberts, Mark
2011
The geometry and dynamics of interacting rigid bodies and point vortices. Zbl 1191.53055
Vankerschaver, Joris; Kanso, Eva; Marsden, Jerrold E.
2009
Tulczyjew triples in higher derivative field theory. Zbl 1367.70062
Grabowska, Katarzyna; Vitagliano, Luca
2015
The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Zbl 1264.05074
Lubowiecki, Paweł; Żołądek, Henryk
2012
A property of conformally Hamiltonian vector fields; application to the Kepler problem. Zbl 1417.37187
Marle, Charles-Michel
2012
A family of compact semitoric systems with two focus-focus singularities. Zbl 1428.37053
Hohloch, Sonja; Palmer, Joseph
2018
Completeness properties of Sobolev metrics on the space of curves. Zbl 1328.58007
Bruveris, Martins
2015
A new multisymplectic unified formalism for second order classical field theories. Zbl 1372.70057
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015
A Hamilton-Jacobi theory on Poisson manifolds. Zbl 1304.70019
de León, Manuel; Martín de Diego, David; Vaquero, Miguel
2014
Shape analysis on Lie groups with applications in computer animation. Zbl 1366.65018
Celledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander
2016
Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations. Zbl 1189.58006
Bucataru, Ioan; Dahl, Matias F.
2009
Sub-Riemannian and sub-Lorentzian geometry on SU(1,1) and on its universal cover. Zbl 1231.53031
Grong, Erlend; Vasil’ev, Alexander
2011
Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach. Zbl 1321.35197
Escher, Joachim; Lyons, Tony
2015
Geometry of matrix decompositions seen through optimal transport and information geometry. Zbl 1368.15010
Modin, Klas
2017
The non-Riemannian dislocated crystal: a tribute to Ekkehart Kröner (1919–2000). Zbl 1281.74029
Van Goethem, Nicolas
2010
On the $$k$$-symplectic, $$k$$-cosymplectic and multisymplectic formalisms of classical field theories. Zbl 1242.70053
Román-Roy, Narciso; Rey, Ángel M.; Salgado, Modesto; Vilariño, Silvia
2011
The emergence of torsion in the continuum limit of distributed edge-dislocations. Zbl 1359.53074
Kupferman, Raz; Maor, Cy
2015
Higher-order variational calculus on Lie algebroids. Zbl 1353.70048
Martínez, Eduardo
2015
Euler equations on a semi-direct product of the diffeomorphisms group by itself. Zbl 1277.37101
Escher, Joachim; Ivanov, Rossen; Kolev, Boris
2011
Local well-posedness of the EPDiff equation: a survey. Zbl 1362.58003
Kolev, Boris
2017
Dirac cotangent bundle reduction. Zbl 1168.70314
Yoshimura, Hiroaki; Marsden, Jerrold E.
2009
Variational principles for spin systems and the Kirchhoff rod. Zbl 1288.70012
Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S.
2009
Computing distances and geodesics between manifold-valued curves in the SRV framework. Zbl 1366.58005
Le Brigant, Alice
2017
Minimal geodesics on $$\mathrm{GL}(n)$$ for left-invariant, right-$$\mathrm O(n)$$-invariant Riemannian metrics. Zbl 1366.53028
Neff, Patrizio; Martin, Robert J.
2016
Second-order constrained variational problems on Lie algebroids: applications to optimal control. Zbl 1410.70020
Colombo, Leonardo
2017
Linear weakly Noetherian constants of motion are horizontal gauge momenta. Zbl 1251.37054
Fassò, Francesco; Giacobbe, Andrea; Sansonetto, Nicola
2012
Models for higher algebroids. Zbl 1330.58015
Jóźwikowski, Michał; Rotkiewicz, Mikołaj
2015
Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups. Zbl 1349.37077
Gay-Balmaz, François; Tronci, Cesare; Vizman, Cornelia
2013
Vector fields with distributions and invariants of ODEs. Zbl 1271.34041
Jakubczyk, Bronisław; Kryński, Wojciech
2013
The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups. Zbl 1330.37061
Eslami Rad, Anahita; Reyes, Enrique G.
2013
Bundle-theoretic methods for higher-order variational calculus. Zbl 1308.58002
Jóźwikowski, Michał; Rotkiewicz, Mikołaj
2014
Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Zbl 1338.37074
Ferrer, Sebastián; Crespo, Francisco
2014
Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Zbl 1281.70028
Ferrer, Sebastián; Lara, Martin
2010
Hamiltonian mechanical systems on Lie algebroids, unimodularity and preservation of volumes. Zbl 1282.53071
Marrero, Juan Carlos
2010
Superposition rules and second-order Riccati equations. Zbl 1225.34015
Cariñena, José F.; de Lucas Araujo, Javier
2011
On the number of weakly Noetherian constants of motion of nonholonomic systems. Zbl 1192.37077
Fassò, Francesco; Giacobbe, Andrea; Sansonetto, Nicola
2009
Higher-order mechanics: variational principles and other topics. Zbl 1284.35014
Prieto-Martínez, Pedro D.; Román-Roy, Narciso
2013
Un-reduction. Zbl 1268.37081
Bruveris, Martins; Ellis, David C. P.; Holm, Darryl D.; Gay-Balmaz, François
2011
Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds. Zbl 1387.70028
Campos, Cédric M.; Guzmán, Elisa; Marrero, Juan Carlos
2012
Tensor products of Dirac structures and interconnection in Lagrangian mechanics. Zbl 1304.70016
Jacobs, Henry O.; Yoshimura, Hiroaki
2014
Kinematic reduction and the Hamilton-Jacobi equation. Zbl 1375.70061
Barbero-Liñán, María; de León, Manuel; Martín de Diego, David; Marrero, Juan C.; Muñoz-Lecanda, Miguel C.
2012
Geometry of plasma dynamics. II: Lie algebra of Hamiltonian vector fields. Zbl 1375.76222
Esen, Oğul; Gümral, Hasan
2012
The leaf space of a multiplicative foliation. Zbl 1266.58006
Jotz, M.
2012
Covariant Hamiltonian field theories on manifolds with boundary: Yang-Mills theories. Zbl 1410.70029
Ibort, Alberto; Spivak, Amelia
2017
When is a control system mechanical? Zbl 1206.93029
Ricardo, Sandra; Respondek, Witold
2010
The stochastic Hamilton-Jacobi equation. Zbl 1278.60104
Lázaro-Camí, Joan-Andreu; Ortega, Juan-Pablo
2009
Geodesic boundary value problems with symmetry. Zbl 1375.49032
Cotter, Colin J.; Holm, Darryl D.
2010
A note on time-optimal paths on perturbed spheroid. Zbl 1405.53061
Kopacz, Piotr
2018
Alternative angle-based approach to the $$\mathcal{KS}$$-map. An interpretation through symmetry and reduction. Zbl 1411.70020
Ferrer, Sebastián; Crespo, Francisco
2018
Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier. Zbl 1359.37124
Crespo, Francisco; Molero, Francisco Javier; Ferrer, Sebastián
2016
Embedded geodesic problems and optimal control for matrix Lie groups. Zbl 1230.49014
Bloch, Anthony M.; Crouch, Peter E.; Nordkvist, Nikolaj; Sanyal, Amit K.
2011
The Toda lattice, old and new. Zbl 1319.37046
Tomei, Carlos
2013
On the extended Euler system and the Jacobi and Weierstrass elliptic functions. Zbl 1326.33027
Crespo, Francisco; Ferrer, Sebastián
2015
Variational reduction of Lagrangian systems with general constraints. Zbl 1257.37033
Grillo, Sergio; Zuccalli, Marcela
2012
Computing metamorphoses between discrete measures. Zbl 1319.49069
Richardson, Casey L.; Younes, Laurent
2013
Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Zbl 1277.70018
Leok, Melvin; Sosa, Diana
2012
Twisted isotropic realisations of twisted Poisson structures. Zbl 1334.37063
Sansonetto, Nicola; Sepe, Daniele
2013
Multi-symplectic method to simulate soliton resonance of $${(2+1)}$$-dimensional Boussinesq equation. Zbl 1277.35111
Hu, Weipeng; Deng, Zichen; Qin, Yuyue
2013
Discriminantly separable polynomials and quad-equations. Zbl 1309.37067
2014
The Hamilton-Jacobi equation, integrability, and nonholonomic systems. Zbl 1304.70018
Bates, Larry M.; Fassò, Francesco; Sansonetto, Nicola
2014
Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings. Zbl 1304.70029
Grabowski, Janusz; Grabowska, Katarzyna; Urbański, Paweł
2014
Nonlinear constraints in nonholonomic mechanics. Zbl 1304.70015
Popescu, Paul; Ida, Cristian
2014
Quotient elastic metrics on the manifold of arc-length parameterized plane curves. Zbl 1365.53002
Tumpach, Alice B.; Preston, Stephen C.
2017
Lagrangian and Hamiltonian formalism in field theory: a simple model. Zbl 1222.70025
Grabowska, Katarzyna
2010
The ubiquity of the symplectic Hamiltonian equations in mechanics. Zbl 1168.70315
Balseiro, P.; de León, M.; Marrero, J. C.; Martín de Diego, D.
2009
The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics. Zbl 1278.70014
Marmo, Giuseppe; Morandi, Giuseppe; Mukunda, Narasimhaiengar
2009
Vortex pairs on a triaxial ellipsoid and Kimura’s conjecture. Zbl 1405.76008
Rodrigues, Adriano Regis; Castilho, César; Koiller, Jair
2018
Invariant nonholonomic Riemannian structures on three-dimensional Lie groups. Zbl 1390.70040
Barrett, Dennis I.; Biggs, Rory; Remsing, Claudiu C.; Rossi, Olga
2016
A weak approach to the stochastic deformation of classical mechanics. Zbl 1375.37175
Lassalle, Rémi; Zambrini, Jean Claude
2016
Lyapunov constraints and global asymptotic stabilization. Zbl 1227.93101
Grillo, Sergio; Marsden, Jerrold E.; Nair, Sujit
2011
A geometric approach to discrete connections on principal bundles. Zbl 1285.53009
Fernández, Javier; Zuccalli, Marcela
2013
Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053
Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A.
2019
On the discretization of nonholonomic dynamics in $$\mathbb{R}^n$$. Zbl 1353.70034
Jiménez, Fernando; Scheurle, Jürgen
2015
On the relation between geometrical quantum mechanics and information geometry. Zbl 1328.53044
Molitor, Mathieu
2015
A note on the Wehrheim-Woodward category. Zbl 1257.53111
Weinstein, Alan
2011
Lagrangian dynamics of submanifolds. Relativistic mechanics. Zbl 1248.53065
2012
Semi-global symplectic invariants of the Euler top. Zbl 1334.37055
2013
Andoyer’s variables and phases in the free rigid body. Zbl 1304.70008
Ferrer, Sebastián; Molero, Francisco J.
2014
An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems. Zbl 1304.70023
Cendra, Hernán; Etchechoury, María; Ferraro, Sebastián J.
2014
Reduction of cluster iteration maps. Zbl 1339.37041
Cruz, Inês; Sousa-Dias, M. Esmeralda
2014
Poisson structures for two nonholonomic systems with partially reduced symmetries. Zbl 1305.70014
Tsiganov, Andrey
2014
The Frank tensor as a boundary condition in intrinsic linearized elasticity. Zbl 1356.35244
Van Goethem, Nicolas
2016
The Tulczyjew triple in mechanics on a Lie group. Zbl 1354.22022
Grabowska, Katarzyna; Zając, Marcin
2016
Invariant sets forced by symmetry. Zbl 1417.37113
Grosshans, Frank D.; Scheurle, Jürgen; Walcher, Sebastian
2012
Hybrid models for perfect complex fluids with multipolar interactions. Zbl 1295.76005
Tronci, Cesare
2012
The Madelung transform as a momentum map. Zbl 1440.53095
Fusca, Daniel
2017
Constraint algorithm for singular field theories in the $$k$$-cosymplectic framework. Zbl 1434.70047
Gràcia, Xavier; Rivas, Xavier; Román-Roy, Narciso
2020
A summary on symmetries and conserved quantities of autonomous Hamiltonian systems. Zbl 1460.37052
Román-Roy, Narciso
2020
Riemann-Hilbert problem, integrability and reductions. Zbl 1431.35053
Gerdjikov, Vladimir S.; Ivanov, Rossen I.; Stefanov, Aleksander A.
2019
Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies. Zbl 1431.74010
Morales, Víctor Manuel Jiménez; De León, Manuel; Epstein, Marcelo
2019
Self-organization on Riemannian manifolds. Zbl 1431.35218
Fetecau, Razvan C.; Zhang, Beril
2019
Relative periodic solutions of the $$n$$-vortex problem on the sphere. Zbl 1433.37054
García-Azpeitia, Carlos
2019
Euler-Lagrangian approach to 3D stochastic Euler equations. Zbl 1435.35290
Flandoli, Franco; Luo, Dejun
2019
Morse families and Dirac systems. Zbl 1439.37060
Barbero Liñán, María; Cendra, Hernán; Toraño, Eduardo García; Martín de Diego, David
2019
Generalized point vortex dynamics on $$\mathbb{CP}^2$$. Zbl 1434.37038
2019
Global well-posedness of a 3D MHD model in porous media. Zbl 1431.76155
Titi, Edriss S.; Trabelsi, Saber
2019
Geometry of Routh reduction. Zbl 1448.70050
Grabowska, Katarzyna; Urbański, Pawel
2019
A geometric perspective on the Piola identity in Riemannian settings. Zbl 1426.53087
Kupferman, Raz; Shachar, Asaf
2019
A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems. Zbl 1426.49050
Jóźwikowski, Michał; Respondek, Witold
2019
A symmetry-adapted numerical scheme for SDEs. Zbl 07168110
De Vecchi, Francesco C.; Romano, Andrea; Ugolini, Stefania
2019
New multisymplectic approach to the metric-affine (Einstein-Palatini) action for gravity. Zbl 1433.83005
Gaset, Jordi; Román-Roy, Narciso
2019
Improving E. Cartan considerations on the invariance of nonholonomic mechanics. Zbl 07168114
Oliva, Waldyr M.; Terra, Gláucio
2019
Riemannian cubics and elastica in the manifold $$\operatorname{SPD}(n)$$ of all $$n\times n$$ symmetric positive-definite matrices. Zbl 1455.53079
Zhang, Erchuan; Noakes, Lyle
2019
Remarks on certain two-component systems with peakon solutions. Zbl 1435.35329
Hay, Mike; Hone, Andrew N. W.; Novikov, Vladimir S.; Wang, Jing Ping
2019
Non-abelian momentum polytopes for products of $$\mathbb{CP}^2$$. Zbl 1434.53091
2019
Momentum maps for mixed states in quantum and classical mechanics. Zbl 1448.81070
Tronci, Cesare
2019
A family of compact semitoric systems with two focus-focus singularities. Zbl 1428.37053
Hohloch, Sonja; Palmer, Joseph
2018
A note on time-optimal paths on perturbed spheroid. Zbl 1405.53061
Kopacz, Piotr
2018
Alternative angle-based approach to the $$\mathcal{KS}$$-map. An interpretation through symmetry and reduction. Zbl 1411.70020
Ferrer, Sebastián; Crespo, Francisco
2018
Vortex pairs on a triaxial ellipsoid and Kimura’s conjecture. Zbl 1405.76008
Rodrigues, Adriano Regis; Castilho, César; Koiller, Jair
2018
Classical field theory on Lie algebroids: multisymplectic formalism. Zbl 1406.58003
Martínez, Eduardo
2018
On the geometry of the Schmidt-Legendre transformation. Zbl 1411.70029
Esen, Oğul; Guha, Partha
2018
A coordinate-free theory of virtual holonomic constraints. Zbl 1428.53022
Consolini, Luca; Costalunga, Alessandro; Maggiore, Manfredi
2018
Lagrange-d’Alembert-Poincaré equations by several stages. Zbl 1407.37087
Cendra, Hernán; Díaz, Viviana A.
2018
Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems. Zbl 1407.37088
Jovanović, Božidar
2018
Bohr-Sommerfeld-Heisenberg quantization of the mathematical pendulum. Zbl 1412.81155
Cushman, Richard; Śniatycki, Jędrzej
2018
Geometry of matrix decompositions seen through optimal transport and information geometry. Zbl 1368.15010
Modin, Klas
2017
Local well-posedness of the EPDiff equation: a survey. Zbl 1362.58003
Kolev, Boris
2017
Computing distances and geodesics between manifold-valued curves in the SRV framework. Zbl 1366.58005
Le Brigant, Alice
2017
Second-order constrained variational problems on Lie algebroids: applications to optimal control. Zbl 1410.70020
Colombo, Leonardo
2017
Covariant Hamiltonian field theories on manifolds with boundary: Yang-Mills theories. Zbl 1410.70029
Ibort, Alberto; Spivak, Amelia
2017
Quotient elastic metrics on the manifold of arc-length parameterized plane curves. Zbl 1365.53002
Tumpach, Alice B.; Preston, Stephen C.
2017
The Madelung transform as a momentum map. Zbl 1440.53095
Fusca, Daniel
2017
About simple variational splines from the Hamiltonian viewpoint. Zbl 1368.65092
Balseiro, Paula; Stuchi, Teresinha J.; Cabrera, Alejandro; Koiller, Jair
2017
Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry. Zbl 1367.53031
Sommer, Stefan; Svane, Anne Marie
2017
On the relationship between the energy shaping and the Lyapunov constraint based methods. Zbl 1373.93248
Grillo, Sergio; Salomone, Leandro; Zuccalli, Marcela
2017
The physical foundations of geometric mechanics. Zbl 1427.70020
Lewis, Andrew D.
2017
Möbius invariants in image recognition. Zbl 1365.53014
2017
Uniform motions in central fields. Zbl 1407.70022
Swaczyna, Martin; Volný, Petr
2017
Complete spelling rules for the Monster tower over three-space. Zbl 1369.58003
Castro, Alex; Howard, Wyatt; Shanbrom, Corey
2017
Shape analysis on Lie groups with applications in computer animation. Zbl 1366.65018
Celledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander
2016
Minimal geodesics on $$\mathrm{GL}(n)$$ for left-invariant, right-$$\mathrm O(n)$$-invariant Riemannian metrics. Zbl 1366.53028
Neff, Patrizio; Martin, Robert J.
2016
Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier. Zbl 1359.37124
Crespo, Francisco; Molero, Francisco Javier; Ferrer, Sebastián
2016
Invariant nonholonomic Riemannian structures on three-dimensional Lie groups. Zbl 1390.70040
Barrett, Dennis I.; Biggs, Rory; Remsing, Claudiu C.; Rossi, Olga
2016
A weak approach to the stochastic deformation of classical mechanics. Zbl 1375.37175
Lassalle, Rémi; Zambrini, Jean Claude
2016
The Frank tensor as a boundary condition in intrinsic linearized elasticity. Zbl 1356.35244
Van Goethem, Nicolas
2016
The Tulczyjew triple in mechanics on a Lie group. Zbl 1354.22022
Grabowska, Katarzyna; Zając, Marcin
2016
The projective symplectic geometry of higher order variational problems: minimality conditions. Zbl 1369.49024
Durán, Carlos; Otero, Diego
2016
Morse theory for elastica. Zbl 1352.58003
2016
Fredholm properties of the $$L^2$$ exponential map on the symplectomorphism group. Zbl 1386.35318
Benn, James
2016
Symplectic reduction at zero angular momentum. Zbl 1341.53116
Cape, Joshua; Herbig, Hans-Christian; Seaton, Christopher
2016
On strain measures and the geodesic distance to $$\mathrm{SO}_n$$ in the general linear group. Zbl 1355.53076
Kupferman, Raz; Shachar, Asaf
2016
Infinitesimally natural principal bundles. Zbl 1350.53063
Janssens, Bas
2016
Free Courant and derived Leibniz pseudoalgebras. Zbl 1388.17003
Jubin, Benoît; Poncin, Norbert; Uchino, Kyosuke
2016
Kirchhoff’s equations of motion via a constrained Zakharov system. Zbl 1418.37109
Shashikanth, Banavara N.
2016
Tulczyjew triples in higher derivative field theory. Zbl 1367.70062
Grabowska, Katarzyna; Vitagliano, Luca
2015
Completeness properties of Sobolev metrics on the space of curves. Zbl 1328.58007
Bruveris, Martins
2015
A new multisymplectic unified formalism for second order classical field theories. Zbl 1372.70057
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015
Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach. Zbl 1321.35197
Escher, Joachim; Lyons, Tony
2015
The emergence of torsion in the continuum limit of distributed edge-dislocations. Zbl 1359.53074
Kupferman, Raz; Maor, Cy
2015
Higher-order variational calculus on Lie algebroids. Zbl 1353.70048
Martínez, Eduardo
2015
Models for higher algebroids. Zbl 1330.58015
Jóźwikowski, Michał; Rotkiewicz, Mikołaj
2015
On the extended Euler system and the Jacobi and Weierstrass elliptic functions. Zbl 1326.33027
Crespo, Francisco; Ferrer, Sebastián
2015
On the discretization of nonholonomic dynamics in $$\mathbb{R}^n$$. Zbl 1353.70034
Jiménez, Fernando; Scheurle, Jürgen
2015
On the relation between geometrical quantum mechanics and information geometry. Zbl 1328.53044
Molitor, Mathieu
2015
Hypersymplectic structures on Courant algebroids. Zbl 1351.53098
Antunes, Paulo; Nunes da Costa, Joana M.
2015
Finiteness of relative equilibria in the planar generalized $$N$$-body problem with fixed subconfigurations. Zbl 1367.70027
Hampton, Marshall; Jensen, Anders Nedergaard
2015
Lie algebroids generated by cohomology operators. Zbl 1330.58014
García-Beltrán, Dennise; Vallejo, José A.; Vorobiev, Yurii
2015
On the control of stability of periodic orbits of completely integrable systems. Zbl 1344.37026
Tudoran, Răzvan M.
2015
A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena. Zbl 1367.70037
Minguzzi, E.
2015
Canonoid and Poissonoid transformations, symmetries and biHamiltonian structures. Zbl 1330.53102
Rastelli, Giovanni; Santoprete, Manuele
2015
Invariant metrics on Lie groups. Zbl 1404.53032
Thompson, Gerard
2015
Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle. Zbl 1308.58005
Escher, Joachim; Kolev, Boris
2014
Higher-order variational problems on Lie groups and optimal control applications. Zbl 1307.70018
Colombo, Leonardo; Martín de Diego, David
2014
A Hamilton-Jacobi theory on Poisson manifolds. Zbl 1304.70019
de León, Manuel; Martín de Diego, David; Vaquero, Miguel
2014
Bundle-theoretic methods for higher-order variational calculus. Zbl 1308.58002
Jóźwikowski, Michał; Rotkiewicz, Mikołaj
2014
Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Zbl 1338.37074
Ferrer, Sebastián; Crespo, Francisco
2014
Tensor products of Dirac structures and interconnection in Lagrangian mechanics. Zbl 1304.70016
Jacobs, Henry O.; Yoshimura, Hiroaki
2014
Discriminantly separable polynomials and quad-equations. Zbl 1309.37067
2014
The Hamilton-Jacobi equation, integrability, and nonholonomic systems. Zbl 1304.70018
Bates, Larry M.; Fassò, Francesco; Sansonetto, Nicola
2014
Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings. Zbl 1304.70029
Grabowski, Janusz; Grabowska, Katarzyna; Urbański, Paweł
2014
Nonlinear constraints in nonholonomic mechanics. Zbl 1304.70015
Popescu, Paul; Ida, Cristian
2014
Andoyer’s variables and phases in the free rigid body. Zbl 1304.70008
Ferrer, Sebastián; Molero, Francisco J.
2014
An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems. Zbl 1304.70023
Cendra, Hernán; Etchechoury, María; Ferraro, Sebastián J.
2014
Reduction of cluster iteration maps. Zbl 1339.37041
Cruz, Inês; Sousa-Dias, M. Esmeralda
2014
Poisson structures for two nonholonomic systems with partially reduced symmetries. Zbl 1305.70014
Tsiganov, Andrey
2014
Fluid-structure interaction in the Lagrange-Poincaré formalism: the Navier-Stokes and inviscid regimes. Zbl 1308.76291
Jacobs, Henry; Vankerschaver, Joris
2014
Periodic orbits in the Kepler-Heisenberg problem. Zbl 1310.53029
Shanbrom, Corey
2014
Aspects of reduction and transformation of Lagrangian systems with symmetry. Zbl 1353.37114
García-Toraño Andrés, E.; Langerock, Bavo; Cantrijn, Frans
2014
Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry. Zbl 1304.70021
Montaldi, James
2014
Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies. Zbl 1347.37100
Grigoryeva, Lyudmila; Ortega, Juan-Pablo; Zub, Stanislav S.
2014
On Euler’s equation and ‘EPDiff’. Zbl 1274.35277
Mumford, David; Michor, Peter W.
2013
Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms. Zbl 1330.37057
Suris, Yuri B.
2013
The supergeometry of Loday algebroids. Zbl 1294.53072
Grabowski, Janusz; Khudaverdyan, David; Poncin, Norbert
2013
Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups. Zbl 1349.37077
Gay-Balmaz, François; Tronci, Cesare; Vizman, Cornelia
2013
Vector fields with distributions and invariants of ODEs. Zbl 1271.34041
Jakubczyk, Bronisław; Kryński, Wojciech
2013
...and 81 more Documents
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#### Cited by 717 Authors

 25 de León Rodríguez, Manuel 24 Bauer, Martin 17 Martín de Diego, David 16 Gay-Balmaz, François 15 Bruveris, Martins 14 Ferrer, Sebastián 13 Holm, Darryl D. 13 Modin, Klas 13 Román-Roy, Narciso 13 Tsyganov, Andreĭ Vladimirovich 12 Crespo, Francisco 12 Esen, Oğul 11 Colombo, Leonardo Jesus 11 Michor, Peter Wolfram 10 García-Naranjo, Luis C. 10 Ratiu, Tudor Stefan 10 Suris, Yuri Borisovich 9 Grabowski, Janusz 9 Sardón, Cristina 9 Van Goethem, Nicolas 8 Kolev, Boris 8 Kupferman, Raz 8 Neff, Patrizio 8 Tronci, Cesare 7 Balseiro, Paula 7 Borisov, Alekseĭ Vladimirovich 7 Bucataru, Ioan 7 Escher, Joachim 7 Grabowska, Katarzyna 7 Grillo, Sergio Daniel 7 Koiller, Jair 7 Leok, Melvin 7 Mestdag, Tom 7 Petrera, Matteo 7 Vialard, François-Xavier 6 Cariñena, José F. 6 Harms, Philipp 6 Jacobs, Henry O. 6 Jiménez, Fernando 6 Maor, Cy 6 Marrero, Juan Carlos 6 Preston, Stephen C. 6 Prieto-Martínez, Pedro Daniel 6 Vankerschaver, Joris 6 Vaquero, Miguel 6 Vilariño, Silvia 6 Yoshimura, Hiroaki 5 Benn, James 5 Bloch, Anthony M. 5 de Lucas, Javier 5 Dragović, Vladimir 5 Gaset, Jordi 5 Guha, Partha 5 Hohloch, Sonja 5 Kryński, Wojciech 5 Mamaev, Ivan Sergeevich 5 Martin, Robert J. 5 Poncin, Norbert 5 Reyes, Enrique G. 5 Zhou, Shouming 4 Arnaudon, Alexis 4 Barbero-Liñán, María 4 Calderón Martín, Antonio Jesús 4 Celledoni, Elena 4 Cendra, Hernán 4 Cismas, Emanuel-Ciprian 4 Cotter, Colin John 4 Durán Fernandez, Carlos Eduardo 4 Ferraro, Sebastián J. 4 Gràcia, Xavier 4 Hochgerner, Simon 4 Jotz, Madeleine 4 Lara, Martín 4 Molero, Francisco Javier 4 Montaldi, James A. 4 Muñoz-Lecanda, Miguel C. 4 Ohsawa, Tomoki 4 Salomone, Leandro M. 4 Sansonetto, Nicola 4 Verdier, Olivier 4 Żołądek, Henryk 4 Zuccalli, Marcela 3 Aldea, Nicoleta 3 Alonso, Jaume 3 Amstutz, Samuel 3 Arguillère, Sylvain 3 Bizyaev, Ivan Alekseevich 3 Bruce, Andrew James 3 Capriotti, Santiago 3 Constantinescu, Oana 3 Covolo, Tiffany 3 Crampin, Mike 3 Cruz, Inês 3 Cruzeiro, Ana-Bela 3 Dullin, Holger R. 3 Epstein, Marcelo 3 Fassò, Francesco 3 Fedorov, Yuri N. 3 García-Toraño Andrés, Eduardo 3 Ghiba, Ionel-Dumitrel ...and 617 more Authors
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#### Cited in 175 Journals

 64 Journal of Geometric Mechanics 45 Journal of Geometry and Physics 33 Journal of Mathematical Physics 28 Journal of Nonlinear Science 26 Regular and Chaotic Dynamics 26 International Journal of Geometric Methods in Modern Physics 17 Differential Geometry and its Applications 14 Archive for Rational Mechanics and Analysis 13 Reports on Mathematical Physics 12 Discrete and Continuous Dynamical Systems 11 Journal of Physics A: Mathematical and Theoretical 9 Journal of Differential Equations 9 Calculus of Variations and Partial Differential Equations 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Communications in Mathematical Physics 8 Nonlinearity 8 Journal of Mathematical Imaging and Vision 7 Foundations of Computational Mathematics 6 Theoretical and Mathematical Physics 6 Monatshefte für Mathematik 6 Annals of Global Analysis and Geometry 6 Nonlinear Analysis. Real World Applications 6 SIAM Journal on Imaging Sciences 5 Celestial Mechanics and Dynamical Astronomy 5 Bulletin des Sciences Mathématiques 5 Journal of Nonlinear Mathematical Physics 5 Theoretical and Applied Mechanics 4 Journal of Mathematical Analysis and Applications 4 Letters in Mathematical Physics 4 SIAM Journal on Mathematical Analysis 4 Indagationes Mathematicae. New Series 4 Journal of Evolution Equations 4 Mediterranean Journal of Mathematics 4 Proceedings of the Steklov Institute of Mathematics 4 Journal of Computational Dynamics 4 Arnold Mathematical Journal 4 European Journal of Mathematics 3 Nuclear Physics. B 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 SIAM Journal on Control and Optimization 3 Acta Applicandae Mathematicae 3 Physica D 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Mathematics and Mechanics of Solids 3 Chaos 3 SIAM Journal on Applied Dynamical Systems 3 Analysis and Mathematical Physics 3 Nelineĭnaya Dinamika 2 Journal of Fluid Mechanics 2 Physics Letters. A 2 BIT 2 Geometriae Dedicata 2 Numerische Mathematik 2 Proceedings of the American Mathematical Society 2 Results in Mathematics 2 Systems & Control Letters 2 Computational Mechanics 2 The Journal of Geometric Analysis 2 Applied Mathematical Modelling 2 Journal of Elasticity 2 Stochastic Processes and their Applications 2 Experimental Mathematics 2 Transformation Groups 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Nonlinear Dynamics 2 Mathematical Physics, Analysis and Geometry 2 Journal of Dynamical and Control Systems 2 Annales Henri Poincaré 2 Qualitative Theory of Dynamical Systems 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Communications in Mathematics 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Information Geometry 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Classical and Quantum Gravity 1 European Journal of Physics 1 General Relativity and Gravitation 1 Inverse Problems 1 Israel Journal of Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Journal of the Franklin Institute 1 Journal of Statistical Physics 1 Linear and Multilinear Algebra 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Letters. B 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Beiträge zur Algebra und Geometrie 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Automatica 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Inventiones Mathematicae 1 Journal of Geometry ...and 75 more Journals
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#### Cited in 55 Fields

 264 Mechanics of particles and systems (70-XX) 237 Differential geometry (53-XX) 216 Dynamical systems and ergodic theory (37-XX) 125 Global analysis, analysis on manifolds (58-XX) 107 Partial differential equations (35-XX) 74 Calculus of variations and optimal control; optimization (49-XX) 59 Numerical analysis (65-XX) 56 Fluid mechanics (76-XX) 45 Ordinary differential equations (34-XX) 43 Mechanics of deformable solids (74-XX) 35 Quantum theory (81-XX) 32 Topological groups, Lie groups (22-XX) 28 Nonassociative rings and algebras (17-XX) 26 Systems theory; control (93-XX) 19 Algebraic geometry (14-XX) 17 Relativity and gravitational theory (83-XX) 16 Probability theory and stochastic processes (60-XX) 15 Statistics (62-XX) 15 Computer science (68-XX) 13 Difference and functional equations (39-XX) 12 Operator theory (47-XX) 12 Information and communication theory, circuits (94-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Several complex variables and analytic spaces (32-XX) 11 Algebraic topology (55-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Functional analysis (46-XX) 9 Manifolds and cell complexes (57-XX) 6 Commutative algebra (13-XX) 6 Associative rings and algebras (16-XX) 5 Biology and other natural sciences (92-XX) 4 History and biography (01-XX) 4 Special functions (33-XX) 4 Approximations and expansions (41-XX) 4 Geometry (51-XX) 3 Combinatorics (05-XX) 3 Group theory and generalizations (20-XX) 3 Real functions (26-XX) 3 Measure and integration (28-XX) 3 Convex and discrete geometry (52-XX) 2 Category theory; homological algebra (18-XX) 2 Potential theory (31-XX) 2 Optics, electromagnetic theory (78-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX)