American Institute of Mathematical Sciences

ISSN:
1941-4889

eISSN:
1941-4897

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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In memory of Geneviève Raugel

Manuel de León, Andrew Lewis and Juan-Pablo Ortega

2020, 12(1) : ⅰ-ⅱ doi: 10.3934/jgm.2020001 +[Abstract](347) +[HTML](179) +[PDF](235.95KB)

Constraint algorithm for singular field theories in the k-cosymplectic framework

Xavier Gràcia, Xavier Rivas and Narciso Román-Roy

2020, 12(1) : 1-23 doi: 10.3934/jgm.2020002 +[Abstract](314) +[HTML](145) +[PDF](460.27KB)

Poisson brackets for the dynamically coupled system of a free boundary and a neutrally buoyant rigid body in a body-fixed frame

Banavara N. Shashikanth

2020, 12(1) : 25-52 doi: 10.3934/jgm.2020003 +[Abstract](279) +[HTML](142) +[PDF](989.99KB)

Rolling and no-slip bouncing in cylinders

Timothy Chumley, Scott Cook, Christopher Cox and Renato Feres

2020, 12(1) : 53-84 doi: 10.3934/jgm.2020004 +[Abstract](301) +[HTML](133) +[PDF](1597.76KB)

De Donder form for second order gravity

Jędrzej Śniatycki and Oǧul Esen

2020, 12(1) : 85-106 doi: 10.3934/jgm.2020005 +[Abstract](283) +[HTML](138) +[PDF](571.97KB)

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](330) +[HTML](162) +[PDF](703.04KB)

Invariant structures on Lie groups

Javier Pérez Álvarez

2020doi: 10.3934/jgm.2020007 +[Abstract](111) +[HTML](70) +[PDF](248.19KB)

Conservative replicator and Lotka-Volterra equations in the context of Dirac\big-isotropic structures

Hassan Najafi Alishah

2020doi: 10.3934/jgm.2020008 +[Abstract](108) +[HTML](58) +[PDF](352.91KB)

A summary on symmetries and conserved quantities of autonomous Hamiltonian systems

Narciso Román-Roy

2020doi: 10.3934/jgm.2020009 +[Abstract](107) +[HTML](55) +[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](97) +[HTML](61) +[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](108) +[HTML](61) +[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](108) +[HTML](67) +[PDF](1212.94KB)

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](3091) +[PDF](475.8KB) ~~Cited By~~(30)

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](2708) +[PDF](789.5KB) ~~Cited By~~(17)

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](3013) +[PDF](661.6KB) ~~Cited By~~(16)

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](3091) +[PDF](318.8KB) ~~Cited By~~(16)

Integrable Euler top and nonholonomic Chaplygin ball

Andrey Tsiganov

2011, 3(3) : 337-362 doi: 10.3934/jgm.2011.3.337 +[Abstract](2385) +[PDF](488.1KB) ~~Cited By~~(15)

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](2533) +[PDF](587.5KB) ~~Cited By~~(15)

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](2426) +[PDF](494.1KB) ~~Cited By~~(14)

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](2458) +[PDF](597.2KB) ~~Cited By~~(14)

$G$-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](2388) +[PDF](272.6KB) ~~Cited By~~(13)

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](2676) +[PDF](360.8KB) ~~Cited By~~(12)

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](2217) +[HTML](348) +[PDF](468.22KB) ~~PDF Downloads~~(167)

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](4170) +[HTML](414) +[PDF](622.49KB) ~~PDF Downloads~~(144)

Classical field theory on Lie algebroids: Multisymplectic formalism

Eduardo Martínez

2018, 10(1) : 93-138 doi: 10.3934/jgm.2018004 +[Abstract](4940) +[HTML](486) +[PDF](708.21KB) ~~PDF Downloads~~(135)

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](330) +[HTML](162) +[PDF](703.04KB) ~~PDF Downloads~~(122)

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](2486) +[HTML](83) +[PDF](680.5KB) ~~PDF Downloads~~(119)

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](2185) +[HTML](270) +[PDF](1374.62KB) ~~PDF Downloads~~(117)

Modified equations for variational integrators applied to Lagrangians linear in velocities

Mats Vermeeren

2019, 11(1) : 1-22 doi: 10.3934/jgm.2019001 +[Abstract](2207) +[HTML](347) +[PDF](1329.23KB) ~~PDF Downloads~~(114)

Geometry of Routh reduction

Katarzyna Grabowska and Paweƚ Urbański

2019, 11(1) : 23-44 doi: 10.3934/jgm.2019002 +[Abstract](2397) +[HTML](360) +[PDF](504.76KB) ~~PDF Downloads~~(113)

The projective Cartan-Klein geometry of the Helmholtz conditions

Carlos Durán and Diego Otero

2018, 10(1) : 69-92 doi: 10.3934/jgm.2018003 +[Abstract](4108) +[HTML](376) +[PDF](437.43KB) ~~PDF Downloads~~(108)

Conservation laws in discrete geometry

Len G. Margolin and Roy S. Baty

2019, 11(2) : 187-203 doi: 10.3934/jgm.2019010 +[Abstract](2397) +[HTML](262) +[PDF](382.02KB) ~~PDF Downloads~~(108)

2018 Impact Factor: 0.525

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