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Volume 12, 2020

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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


Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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Invariant structures on Lie groups
Javier Pérez Álvarez
2020, 12(2) : 141-148 doi: 10.3934/jgm.2020007 +[Abstract](544) +[HTML](287) +[PDF](270.72KB)
Conservative replicator and Lotka-Volterra equations in the context of Dirac\big-isotropic structures
Hassan Najafi Alishah
2020, 12(2) : 149-164 doi: 10.3934/jgm.2020008 +[Abstract](539) +[HTML](250) +[PDF](368.78KB)
Nonholonomic and constrained variational mechanics
Andrew D. Lewis
2020, 12(2) : 165-308 doi: 10.3934/jgm.2020013 +[Abstract](431) +[HTML](145) +[PDF](1063.2KB)
A note on Hybrid Routh reduction for time-dependent Lagrangian systems
Leonardo J. Colombo, María Emma Eyrea Irazú and Eduardo García-Toraño Andrés
2020, 12(2) : 309-321 doi: 10.3934/jgm.2020014 +[Abstract](277) +[HTML](105) +[PDF](401.58KB)
A summary on symmetries and conserved quantities of autonomous Hamiltonian systems
Narciso Román-Roy
2020doi: 10.3934/jgm.2020009 +[Abstract](400) +[HTML](237) +[PDF](333.78KB)
The group of symplectic birational maps of the plane and the dynamics of a family of 4D maps
Inês Cruz, Helena Mena-Matos and Esmeralda Sousa-Dias
2020doi: 10.3934/jgm.2020010 +[Abstract](637) +[HTML](229) +[PDF](341.88KB)
Symmetry reduction of the 3-body problem in $ \mathbb{R}^4 $
Holger R. Dullin and Jürgen Scheurle
2020doi: 10.3934/jgm.2020011 +[Abstract](407) +[HTML](234) +[PDF](457.44KB)
Relative equilibria of the 3-body problem in $ \mathbb{R}^4 $
Alain Albouy and Holger R. Dullin
2020doi: 10.3934/jgm.2020012 +[Abstract](422) +[HTML](261) +[PDF](1212.94KB)
The method of averaging for Poisson connections on foliations and its applications
Misael Avendaño-Camacho, Isaac Hasse-Armengol, Eduardo Velasco-Barreras and Yury Vorobiev
2020doi: 10.3934/jgm.2020015 +[Abstract](254) +[HTML](99) +[PDF](351.58KB)
A unifying approach for rolling symmetric spaces
Krzysztof A. Krakowski, Luís Machado and Fátima Silva Leite
2020doi: 10.3934/jgm.2020016 +[Abstract](207) +[HTML](114) +[PDF](1284.64KB)
A family of multiply warped product semi-riemannian einstein metrics
Buddhadev Pal and Pankaj Kumar
2020doi: 10.3934/jgm.2020017 +[Abstract](75) +[HTML](33) +[PDF](378.15KB)
Getting into the vortex: On the contributions of james montaldi
Jair Koiller
2020doi: 10.3934/jgm.2020018 +[Abstract](17) +[HTML](12) +[PDF](1585.21KB)
Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy
Miguel Rodríguez-Olmos
2020doi: 10.3934/jgm.2020019 +[Abstract](71) +[HTML](33) +[PDF](393.52KB)
Some remarks about the centre of mass of two particles in spaces of constant curvature
Luis C. García-Naranjo
2020doi: 10.3934/jgm.2020020 +[Abstract](63) +[HTML](30) +[PDF](635.68KB)
Angular momentum coupling, Dirac oscillators, and quantum band rearrangements in the presence of momentum reversal symmetries
Toshihiro Iwai, Dmitrií A. Sadovskií and Boris I. Zhilinskií
2020doi: 10.3934/jgm.2020021 +[Abstract](78) +[HTML](35) +[PDF](936.86KB)
Control of locomotion systems and dynamics in relative periodic orbits
Francesco Fassò, Simone Passarella and Marta Zoppello
2020doi: 10.3934/jgm.2020022 +[Abstract](71) +[HTML](29) +[PDF](848.92KB)
On nomalized differentials on spectral curves associated with the sinh-gordon equation
Thomas Kappeler and Yannick Widmer
2020doi: 10.3934/jgm.2020023 +[Abstract](56) +[HTML](28) +[PDF](1833.79KB)
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](3467) +[PDF](475.8KB) Cited By(42)
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](2857) +[PDF](587.5KB) Cited By(25)
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](3422) +[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](3069) +[PDF](789.5KB) Cited By(21)
Integrable Euler top and nonholonomic Chaplygin ball
Andrey Tsiganov
2011, 3(3) : 337-362 doi: 10.3934/jgm.2011.3.337 +[Abstract](2712) +[PDF](488.1KB) Cited By(20)
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](3027) +[PDF](360.8KB) Cited By(20)
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](3432) +[PDF](318.8KB) Cited By(17)
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](2681) +[PDF](494.1KB) Cited By(17)
$G$-Chaplygin systems with internal symmetries, truncation, and an (almost) symplectic view of Chaplygin's ball
Simon Hochgerner and Luis García-Naranjo
2009, 1(1) : 35-53 doi: 10.3934/jgm.2009.1.35 +[Abstract](2645) +[PDF](272.6KB) Cited By(17)
Shape analysis on Lie groups with applications in computer animation
Elena Celledoni, Markus Eslitzbichler and Alexander Schmeding
2016, 8(3) : 273-304 doi: 10.3934/jgm.2016008 +[Abstract](2375) +[PDF](3465.1KB) Cited By(15)
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](3609) +[HTML](393) +[PDF](468.22KB) PDF Downloads(239)
Lagrange-d'alembert-poincaré equations by several stages
Hernán Cendra and Viviana A. Díaz
2018, 10(1) : 1-41 doi: 10.3934/jgm.2018001 +[Abstract](5434) +[HTML](456) +[PDF](622.49KB) PDF Downloads(159)
Invariant metrics on Lie groups
Gerard Thompson
2015, 7(4) : 517-526 doi: 10.3934/jgm.2015.7.517 +[Abstract](2528) +[PDF](369.5KB) PDF Downloads(158)
On the degenerate boussinesq equations on surfaces
Siran Li, Jiahong Wu and Kun Zhao
2020, 12(1) : 107-140 doi: 10.3934/jgm.2020006 +[Abstract](1161) +[HTML](248) +[PDF](703.04KB) PDF Downloads(149)
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](3458) +[HTML](318) +[PDF](1374.62KB) PDF Downloads(148)
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](2084) +[HTML](54) +[PDF](609.1KB) PDF Downloads(148)
Classical field theory on Lie algebroids: Multisymplectic formalism
Eduardo Martínez
2018, 10(1) : 93-138 doi: 10.3934/jgm.2018004 +[Abstract](6246) +[HTML](541) +[PDF](708.21KB) PDF Downloads(147)
Conservation laws in discrete geometry
Len G. Margolin and Roy S. Baty
2019, 11(2) : 187-203 doi: 10.3934/jgm.2019010 +[Abstract](3693) +[HTML](304) +[PDF](382.02KB) PDF Downloads(142)
A note on time-optimal paths on perturbed spheroid
Piotr Kopacz
2018, 10(2) : 139-172 doi: 10.3934/jgm.2018005 +[Abstract](3768) +[HTML](325) +[PDF](3595.86KB) PDF Downloads(137)
Second-order constrained variational problems on Lie algebroids: Applications to Optimal Control
Leonardo Colombo
2017, 9(1) : 1-45 doi: 10.3934/jgm.2017001 +[Abstract](2822) +[HTML](131) +[PDF](680.5KB) PDF Downloads(136)

2019  Impact Factor: 0.649

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