ISSN:
 1941-4889

eISSN:
 1941-4897

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Volume 9, 2017

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Volume 7, 2015

Volume 6, 2014

Volume 5, 2013

Volume 4, 2012

Volume 3, 2011

Volume 2, 2010

Volume 1, 2009

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

More detailed information on the subjects covered by the journal can be found by viewing the fields of research of the members of the editorial board.

Contributions to this journal are published free of charge.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in March, June, September and December.
  • Publishes online only.
  • Indexed in Science Citation Index-Expanded, CompuMath Citation Index, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), INSPEC, Mathematical Reviews, MathSciNet, PASCAL/CNRS, Scopus, Web of Science and Zentralblatt MATH.
  • Archived in Portico and CLOCKSS.
  • JGM is a publication of the American Institute of Mathematical Sciences with the support of the Consejo Superior de Investigaciones Científicas (CSIC). All rights reserved.

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

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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](410) +[HTML](235) +[PDF](622.49KB)
Abstract:

The aim of this paper is to write explicit expression in terms of a given principal connection of the Lagrange-d'Alembert-Poincaré equations by several stages. This is obtained by using a reduced Lagrange-d'Alembert's Principle by several stages, extending methods known for the case of one stage in the previous literature. The case of Euler's disk is described as an illustrative example.

On some aspects of the discretization of the suslov problem
Fernando Jiménez and Jürgen Scheurle
2018, 10(1) : 43-68 doi: 10.3934/jgm.2018002 +[Abstract](300) +[HTML](194) +[PDF](1325.47KB)
Abstract:

In this paper we explore the discretization of Euler-Poincaré-Suslov equations on SO(3), i.e. of the Suslov problem. We show that the consistency order corresponding to the unreduced and reduced setups, when the discrete reconstruction equation is given by a Cayley retraction map, are related to each other in a nontrivial way. We give precise conditions under which general and variational integrators generate a discrete flow preserving the constraint distribution. We establish general consistency bounds and illustrate the performance of several discretizations by some plots. Moreover, along the lines of [15] we show that any constraints-preserving discretization may be understood as being generated by the exact evolution map of a time-periodic non-autonomous perturbation of the original continuous-time nonholonomic system.

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](300) +[HTML](196) +[PDF](437.43KB)
Abstract:

We show that the Helmholtz conditions characterizing differential equations arising from variational problems can be expressed in terms of invariants of curves in a suitable Grassmann manifold.

Classical field theory on Lie algebroids: Multisymplectic formalism
Eduardo Martínez
2018, 10(1) : 93-138 doi: 10.3934/jgm.2018004 +[Abstract](352) +[HTML](281) +[PDF](708.21KB)
Abstract:

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a Lagrangian function is given, we find the equations of motion in terms of a Cartan form canonically associated to the Lagrangian. The Hamiltonian formalism is also extended to this setting and we find the relation between the solutions of both formalism. When the first Lie algebroid is a tangent bundle we give a variational description of the equations of motion. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincaré and Lagrange Poincaré cases), variational problems for holomorphic maps, Sigma models or Chern-Simons theories. One of the advantages of our theory is that it is based in the existence of a multisymplectic form on a Lie algebroid.

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](394) +[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](312) +[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](280) +[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](379) +[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](259) +[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](335) +[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](329) +[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](325) +[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](340) +[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](311) +[PDF](360.8KB) Cited By(12)
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](410) +[HTML](235) +[PDF](622.49KB) PDF Downloads(87)
Classical field theory on Lie algebroids: Multisymplectic formalism
Eduardo Martínez
2018, 10(1) : 93-138 doi: 10.3934/jgm.2018004 +[Abstract](352) +[HTML](281) +[PDF](708.21KB) PDF Downloads(86)
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](300) +[HTML](196) +[PDF](437.43KB) PDF Downloads(63)
On some aspects of the discretization of the suslov problem
Fernando Jiménez and Jürgen Scheurle
2018, 10(1) : 43-68 doi: 10.3934/jgm.2018002 +[Abstract](300) +[HTML](194) +[PDF](1325.47KB) PDF Downloads(55)
The physical foundations of geometric mechanics
Andrew D. Lewis
2017, 9(4) : 487-574 doi: 10.3934/jgm.2017019 +[Abstract](693) +[HTML](138) +[PDF](2331.7KB) PDF Downloads(21)
On a geometric framework for Lagrangian supermechanics
Andrew James Bruce, Katarzyna Grabowska and Giovanni Moreno
2017, 9(4) : 411-437 doi: 10.3934/jgm.2017016 +[Abstract](456) +[HTML](113) +[PDF](531.9KB) PDF Downloads(13)
On the relationship between the energy shaping and the Lyapunov constraint based methods
Sergio Grillo, Leandro Salomone and Marcela Zuccalli
2017, 9(4) : 459-486 doi: 10.3934/jgm.2017018 +[Abstract](239) +[HTML](115) +[PDF](568.6KB) PDF Downloads(9)
About simple variational splines from the Hamiltonian viewpoint
Paula Balseiro, Teresinha J. Stuchi, Alejandro Cabrera and Jair Koiller
2017, 9(3) : 257-290 doi: 10.3934/jgm.2017011 +[Abstract](277) +[HTML](10) +[PDF](2543.9KB) PDF Downloads(5)
On the relation between geometrical quantum mechanics and information geometry
Mathieu Molitor
2015, 7(2) : 169-202 doi: 10.3934/jgm.2015.7.169 +[Abstract](325) +[PDF](660.3KB) PDF Downloads(5)
A Hamilton-Jacobi theory on Poisson manifolds
Manuel de León, David Martín de Diego and Miguel Vaquero
2014, 6(1) : 121-140 doi: 10.3934/jgm.2014.6.121 +[Abstract](325) +[PDF](443.8KB) PDF Downloads(5)

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