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JGM Flyer: showing all essential information of the journal.
The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal:

1. Lagrangian and Hamiltonian mechanics
2. Symplectic and Poisson geometry and their applications to mechanics
3. Geometric and optimal control theory
4. Geometric and variational integration
5. Geometry of stochastic systems
6. Geometric methods in dynamical systems
7. Continuum mechanics
8. Classical field theory
9. Fluid mechanics
10. Infinite-dimensional dynamical systems
11. Quantum mechanics and quantum information theory
12. Applications in physics, technology, engineering and the biological sciences


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Preface to special issue in honor of Kirill C. H. Mackenzie
Iakovos Androulidakis, Henrique Bursztyn, Juan-Carlos Marrero and Alan Weinstein
2021, 13(3) : ⅰ-ⅸ doi: 10.3934/jgm.2021025 +[Abstract](35) +[HTML](15) +[PDF](782.1KB)
Book review: General theory of Lie groupoids and Lie algebroids, by Kirill C. H. Mackenzie
Theodore Voronov
2021, 13(3) : 277-283 doi: 10.3934/jgm.2021026 +[Abstract](24) +[HTML](8) +[PDF](106.24KB)
Symplectic $ {\mathbb Z}_2^n $-manifolds
Andrew James Bruce and Janusz Grabowski
2021, 13(3) : 285-311 doi: 10.3934/jgm.2021020 +[Abstract](189) +[HTML](69) +[PDF](501.65KB)
On twistor almost complex structures
Michel Cahen, Simone Gutt and John Rawnsley
2021, 13(3) : 313-331 doi: 10.3934/jgm.2021006 +[Abstract](388) +[HTML](217) +[PDF](399.89KB)
Schwinger's picture of quantum mechanics: 2-groupoids and symmetries
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo and Luca Schiavone
2021, 13(3) : 333-354 doi: 10.3934/jgm.2021008 +[Abstract](337) +[HTML](154) +[PDF](576.05KB)
Local and global integrability of Lie brackets
Rui L. Fernandes and Yuxuan Zhang
2021, 13(3) : 355-384 doi: 10.3934/jgm.2021024 +[Abstract](103) +[HTML](37) +[PDF](464.74KB)
On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras
Johannes Huebschmann
2021, 13(3) : 385-402 doi: 10.3934/jgm.2021009 +[Abstract](450) +[HTML](232) +[PDF](381.35KB)
Transitive double Lie algebroids via core diagrams
Madeleine Jotz Lean and Kirill C. H. Mackenzie
2021, 13(3) : 403-457 doi: 10.3934/jgm.2021023 +[Abstract](151) +[HTML](60) +[PDF](673.58KB)
From Schouten to Mackenzie: Notes on brackets
Yvette Kosmann-Schwarzbach
2021, 13(3) : 459-476 doi: 10.3934/jgm.2021013 +[Abstract](191) +[HTML](115) +[PDF](387.04KB)
Local convexity for second order differential equations on a Lie algebroid
Juan Carlos Marrero, David Martín de Diego and Eduardo Martínez
2021, 13(3) : 477-499 doi: 10.3934/jgm.2021021 +[Abstract](139) +[HTML](65) +[PDF](410.65KB)
Brackets by any other name
Jim Stasheff
2021, 13(3) : 501-516 doi: 10.3934/jgm.2021014 +[Abstract](184) +[HTML](121) +[PDF](360.11KB)
Multi-agent systems for quadcopters
Richard Carney, Monique Chyba, Chris Gray, George Wilkens and Corey Shanbrom
2021doi: 10.3934/jgm.2021005 +[Abstract](402) +[HTML](195) +[PDF](3380.67KB)
From Schouten to Mackenzie: Notes on brackets
Yvette Kosmann-Schwarzbach
2021doi: 10.3934/jgm.2021010 +[Abstract](346) +[HTML](182) +[PDF](357.64KB)
Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations
Jacky Cresson, Fernando Jiménez and Sina Ober-Blöbaum
2021doi: 10.3934/jgm.2021012 +[Abstract](203) +[HTML](97) +[PDF](514.5KB)
Holonomy transformations for Lie subalgebroids
Marco Zambon
2021doi: 10.3934/jgm.2021016 +[Abstract](168) +[HTML](81) +[PDF](449.51KB)
Error analysis of forced discrete mechanical systems
Javier Fernández, Sebastián Elías Graiff Zurita and Sergio Grillo
2021doi: 10.3934/jgm.2021017 +[Abstract](159) +[HTML](69) +[PDF](796.61KB)
On computational Poisson geometry I: Symbolic foundations
Miguel Ángel Evangelista-Alvarado, José Crispín Ruíz-Pantaleón and Pablo Suárez-Serrato
2021doi: 10.3934/jgm.2021018 +[Abstract](171) +[HTML](76) +[PDF](466.22KB)
Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations
Willy Sarlet and Tom Mestdag
2021doi: 10.3934/jgm.2021019 +[Abstract](153) +[HTML](62) +[PDF](307.03KB)
Explicit solutions of the kinetic and potential matching conditions of the energy shaping method
Sergio Grillo, Leandro Salomone and Marcela Zuccalli
2021doi: 10.3934/jgm.2021022 +[Abstract](148) +[HTML](55) +[PDF](460.76KB)
Sobolev metrics on shape space of surfaces
Martin Bauer, Philipp Harms and Peter W. Michor
2011, 3(4) : 389-438 doi: 10.3934/jgm.2011.3.389 +[Abstract](4805) +[PDF](2091.6KB) Cited By(47)
Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics
Manuel de León, Juan Carlos Marrero and David Martín de Diego
2010, 2(2) : 159-198 doi: 10.3934/jgm.2010.2.159 +[Abstract](4483) +[PDF](475.8KB) Cited By(45)
Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle
Joachim Escher and Boris Kolev
2014, 6(3) : 335-372 doi: 10.3934/jgm.2014.6.335 +[Abstract](3683) +[PDF](587.5KB) Cited By(27)
On Euler's equation and 'EPDiff'
David Mumford and Peter W. Michor
2013, 5(3) : 319-344 doi: 10.3934/jgm.2013.5.319 +[Abstract](4690) +[PDF](661.6KB) Cited By(23)
Nonholonomic Hamilton-Jacobi equation and integrability
Tomoki Ohsawa and Anthony M. Bloch
2009, 1(4) : 461-481 doi: 10.3934/jgm.2009.1.461 +[Abstract](3981) +[PDF](789.5KB) Cited By(22)
Geodesic Vlasov equations and their integrable moment closures
Darryl D. Holm and Cesare Tronci
2009, 1(2) : 181-208 doi: 10.3934/jgm.2009.1.181 +[Abstract](3989) +[PDF](360.8KB) Cited By(22)
Integrable Euler top and nonholonomic Chaplygin ball
Andrey Tsiganov
2011, 3(3) : 337-362 doi: 10.3934/jgm.2011.3.337 +[Abstract](3642) +[PDF](488.1KB) Cited By(20)
Clebsch optimal control formulation in mechanics
François Gay-Balmaz and Tudor S. Ratiu
2011, 3(1) : 41-79 doi: 10.3934/jgm.2011.3.41 +[Abstract](3760) +[PDF](597.2KB) Cited By(20)
Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
Andrew N. W. Hone and Matteo Petrera
2009, 1(1) : 55-85 doi: 10.3934/jgm.2009.1.55 +[Abstract](3484) +[PDF](494.1KB) Cited By(18)
Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
Ioan Bucataru and Matias F. Dahl
2009, 1(2) : 159-180 doi: 10.3934/jgm.2009.1.159 +[Abstract](4507) +[PDF](318.8KB) Cited By(17)
Invariant metrics on Lie groups
Gerard Thompson
2015, 7(4) : 517-526 doi: 10.3934/jgm.2015.7.517 +[Abstract](3550) +[PDF](369.5KB) PDF Downloads(765)
Probability measures on infinite-dimensional Stiefel manifolds
Eleonora Bardelli and Andrea Carlo Giuseppe Mennucci
2017, 9(3) : 291-316 doi: 10.3934/jgm.2017012 +[Abstract](3031) +[HTML](62) +[PDF](609.1KB) PDF Downloads(540)
Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena
Sergio Albeverio and Sonia Mazzucchi
2019, 11(2) : 123-137 doi: 10.3934/jgm.2019006 +[Abstract](4957) +[HTML](397) +[PDF](468.22KB) PDF Downloads(481)
Riemannian cubics and elastica in the manifold $ \operatorname{SPD}(n) $ of all $ n\times n $ symmetric positive-definite matrices
Erchuan Zhang and Lyle Noakes
2019, 11(2) : 277-299 doi: 10.3934/jgm.2019015 +[Abstract](4540) +[HTML](324) +[PDF](1374.62KB) PDF Downloads(377)
A summary on symmetries and conserved quantities of autonomous Hamiltonian systems
Narciso Román-Roy
2020, 12(3) : 541-551 doi: 10.3934/jgm.2020009 +[Abstract](1361) +[HTML](374) +[PDF](349.98KB) PDF Downloads(376)
The principle of virtual work and Hamilton's principle on Galilean manifolds
Giuseppe Capobianco, Tom Winandy and Simon R. Eugster
2021, 13(2) : 167-193 doi: 10.3934/jgm.2021002 +[Abstract](695) +[HTML](279) +[PDF](431.64KB) PDF Downloads(330)
Vortex pairs on a triaxial ellipsoid and Kimura's conjecture
Adriano Regis Rodrigues, César Castilho and Jair Koiller
2018, 10(2) : 189-208 doi: 10.3934/jgm.2018007 +[Abstract](4131) +[HTML](266) +[PDF](1421.47KB) PDF Downloads(328)
Invariant structures on Lie groups
Javier Pérez Álvarez
2020, 12(2) : 141-148 doi: 10.3934/jgm.2020007 +[Abstract](1848) +[HTML](318) +[PDF](270.72KB) PDF Downloads(298)
The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics
Giuseppe Marmo, Giuseppe Morandi and Narasimhaiengar Mukunda
2009, 1(3) : 317-355 doi: 10.3934/jgm.2009.1.317 +[Abstract](2931) +[PDF](533.9KB) PDF Downloads(278)
Momentum maps for mixed states in quantum and classical mechanics
Cesare Tronci
2019, 11(4) : 639-656 doi: 10.3934/jgm.2019032 +[Abstract](1844) +[HTML](173) +[PDF](401.35KB) PDF Downloads(275)

2020 Impact Factor: 0.857
5 Year Impact Factor: 0.807
2020 CiteScore: 1.3

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