ISSN:
 1941-4889

eISSN:
 1941-4897

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Volume 10, 2018

Volume 9, 2017

Volume 8, 2016

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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On the geometry of the Schmidt-Legendre transformation
Oğul Esen and Partha Guha
2018, 10(3) : 251-291 doi: 10.3934/jgm.2018010 +[Abstract](127) +[HTML](34) +[PDF](674.71KB)
Abstract:

Tulczyjew's triples are constructed for the Schmidt-Legendre transformations of both second and third-order Lagrangians. Symplectic diffeomorphisms relating the Ostrogradsky-Legendre and the Schmidt-Legendre transformations are derived. Several examples are presented.

The Euler-Poisson equations: An elementary approach to integrability conditions
Sasho Popov and Jean-Marie Strelcyn
2018, 10(3) : 293-329 doi: 10.3934/jgm.2018011 +[Abstract](132) +[HTML](69) +[PDF](564.97KB)
Abstract:

We consider the Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point with parameters in a complex domain. We suppose that these equations admit a first integral functionally independent of the three already known integrals which does not depend on all the variables. We prove that this may happen only in the already known three integrable cases or in the trivial case of kinetic symmetry. We provide a method for finding such a fourth integral, when it exists.

A family of compact semitoric systems with two focus-focus singularities
Sonja Hohloch and Joseph Palmer
2018, 10(3) : 331-357 doi: 10.3934/jgm.2018012 +[Abstract](72) +[HTML](37) +[PDF](5451.01KB)
Abstract:

About 6 years ago, semitoric systems were classified by Pelayo & Vũ Ngọc by means of five invariants. Standard examples are the coupled spin oscillator on \begin{document}$\mathbb{S}^2 \times \mathbb{R}^2$\end{document} and coupled angular momenta on \begin{document}$\mathbb{S}^2 \times \mathbb{S}^2$\end{document}, both having exactly one focus-focus singularity. But so far there were no explicit examples of systems with more than one focus-focus singularity which are semitoric in the sense of that classification. This paper introduces a \begin{document}$6$\end{document}-parameter family of integrable systems on \begin{document}$\mathbb{S}^2 \times \mathbb{S}^2$\end{document} and proves that, for certain ranges of the parameters, it is a compact semitoric system with precisely two focus-focus singularities. Since the twisting index (one of the semitoric invariants) is related to the relationship between different focus-focus points, this paper provides systems for the future study of the twisting index.

Alternative angle-based approach to the $\mathcal{KS}$-Map. An interpretation through symmetry and reduction
Sebastián Ferrer and Francisco Crespo
2018, 10(3) : 359-372 doi: 10.3934/jgm.2018013 +[Abstract](83) +[HTML](37) +[PDF](379.97KB)
Abstract:

The \begin{document}$\mathcal{KS}$\end{document} map is revisited in terms of an \begin{document}$S^1$\end{document}-action in \begin{document}$T^*\mathbb{H}_0$\end{document} with the bilinear function as the associated momentum map. Indeed, the \begin{document}$\mathcal{KS}$\end{document} transformation maps the \begin{document}$S^1$\end{document}-fibers related to the mentioned action to single points. By means of this perspective a second twin-bilinear function is obtained with an analogous \begin{document}$S^1$\end{document}-action. We also show that the connection between the 4-D isotropic harmonic oscillator and the spatial Kepler systems can be done in a straightforward way after regularization and through the extension to 4 degrees of freedom of the Euler angles, when the bilinear relation is imposed. This connection incorporates both bilinear functions among the variables. We will show that an alternative regularization separates the oscillator expressed in Projective Euler variables. This setting takes advantage of the two bilinear functions and another integral of the system including them among a new set of variables that allows to connect the 4-D isotropic harmonic oscillator and the planar Kepler system. In addition, our approach makes transparent that only when we refer to rectilinear solutions, both bilinear relations defining the \begin{document}$\mathcal{KS}$\end{document} transformations are needed.

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](829) +[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](704) +[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](667) +[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](757) +[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](620) +[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](679) +[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](711) +[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](671) +[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](709) +[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](677) +[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](740) +[HTML](353) +[PDF](622.49KB) PDF Downloads(118)
Classical field theory on Lie algebroids: Multisymplectic formalism
Eduardo Martínez
2018, 10(1) : 93-138 doi: 10.3934/jgm.2018004 +[Abstract](691) +[HTML](425) +[PDF](708.21KB) PDF Downloads(116)
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](613) +[HTML](317) +[PDF](437.43KB) PDF Downloads(86)
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](572) +[HTML](299) +[PDF](1325.47KB) PDF Downloads(75)
A note on time-optimal paths on perturbed spheroid
Piotr Kopacz
2018, 10(2) : 139-172 doi: 10.3934/jgm.2018005 +[Abstract](415) +[HTML](257) +[PDF](3595.86KB) PDF Downloads(62)
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](277) +[HTML](206) +[PDF](1421.47KB) PDF Downloads(50)
The physical foundations of geometric mechanics
Andrew D. Lewis
2017, 9(4) : 487-574 doi: 10.3934/jgm.2017019 +[Abstract](1214) +[HTML](254) +[PDF](2331.7KB) PDF Downloads(47)
Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems
Božzidar Jovanović
2018, 10(2) : 173-187 doi: 10.3934/jgm.2018006 +[Abstract](274) +[HTML](140) +[PDF](440.5KB) PDF Downloads(46)
A note on the normalization of generating functions
Simone Vazzoler
2018, 10(2) : 209-215 doi: 10.3934/jgm.2018008 +[Abstract](239) +[HTML](197) +[PDF](297.83KB) PDF Downloads(40)
Double groupoids and the symplectic category
Santiago Cañez
2018, 10(2) : 217-250 doi: 10.3934/jgm.2018009 +[Abstract](254) +[HTML](159) +[PDF](485.27KB) PDF Downloads(39)

2017  Impact Factor: 0.561

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