# Recent publications

* A number of articles can be downloaded as postscript - [ps] or
Portable Document Format - [PDF] files. PS- or PDF-files can be opened
with respecively Ghostview or Acrobat Reader
*

2011 2010 2009 2008 |
2007 2006 2005 2004 |
2003 2002 2001 2000 |
1999 1998 1997 1996 |
1995 1994 1993 1992 |

### Preprints

M. Crampin and T. Mestdag, The Cartan form for constrained Lagrangian systems and the
nonholonomic Noether theorem.

[arXiv]

M. Crampin and T. Mestdag, Reduction of invariant constrained systems using anholonomic frames.

[arXiv]

J. Vankerschaver, H. Yoshimura, J. E. Marsden.
Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac
Structures. Submitted to Proc. 49th Control and Decision Conference.

[pdf]

### 2011

T. Mestdag, W. Sarlet and M. Crampin, The inverse problem for Lagrangian systems with certain
non-conservative forces. To appear in Diff. Geom. Appl.

[pdf]

### 2010

B. Langerock and M. Castrillon Lopez, Routh reduction for singular Lagrangians, IJGMMP 7(8), 1451--1489 (2010).

[ArXiv] [doi]

W. Sarlet, Comment on 'Conservation laws of
higher-order nonlinear PDEs and the variational conservation laws in the
class with mixed derivatives'. J. Phys. A: Math. Theor. 43 (2010)
458001.

[pdf] [doi]

W. Sarlet and G. Prince, Alternative kinetic energy metrics for Lagrangian systems, J. Phys. A: Math. Theor. 43 (2010) 445204.

[pdf] [doi]

J. Vankerschaver, E. Kanso, J. E. Marsden. The Dynamics
of a Rigid Body in Potential Flow with Circulation, Reg. Chaot. Dyn. 15
(2010) 606-629.

[pdf]

T. Mestdag and M. Crampin, Nonholonomic systems as
restricted Euler-Lagrange systems, Balkan J. Geom. Appl. 15 (2) (2010),
78-89.

[pdf]

M. Crampin, T. Mestdag and W. Sarlet,
On the generalized Helmholtz conditions for Lagrangian systems with
dissipative forces, Z. Angew. Math. Mech. 90 (2010), 502--508.

[pdf]

M. Crampin and T. Mestdag, Anholonomic frames in constrained dynamics, Dynamical Systems 25 (2010), 159 - 187.

[pdf]

B. Langerock, F. Cantrijn and J. Vankerschaver,
Routhian reduction for quasi-invariant Lagrangians. J. Math. Phys. 51
(2010) 02290.

[pdf]

### 2009

C.M. Campos, M. de Leon, D. Martin de Diego and J.
Vankerschaver, Unambiguous Formalism for Higher-Order Lagrangian Field
Theories. J. Phys. A: Math. Theor. 42 (2009) 475207.

[pdf]

O.E. Fernandez, T. Mestdag and A.M. Bloch, A
generalization of Chaplygin's reducibility theorem. Reg. Chaot. Dyn. 14
(2009), 635-655.

[pdf]

Y. Or, J. Vankerschaver, S.D. Kelly, R.M. Murray and
J.E. Marsden, Geometric Control of Particle Manipulation in a
Two-Dimensional Fluid.
Proc. 48th Control and Decision Conf, Shanghai (2009).

[pdf]

W. Sarlet, G.E. Prince and M. Crampin, Generalized
submersiveness of second-order ordinary differential equations, J. Geom.
Mech. 1 (2009) 209-221.

[pdf]

J. Vankerschaver, E. Kanso, J.E. Marsden: The Geometry and Dynamics of Interacting Rigid
Bodies and Point Vortices. J. Geom. Mech. 1 (2009) 223-266.

[pdf]

M. Crampin and T. Mestdag, Second-order differential equation fields with symmetry.
In: O. Krupkova et al (eds.), Variations, Geometry and Physics, Nova Science Publishers
(2009), 261-275.

[pdf]

W. Sarlet, Linear connections along the tangent bundle
projection. In: O. Krupkova et al (eds.), Variations, Geometry and
Physics, Nova Science Publishers
(2009), 315-340.

[pdf]

T. Mestdag, A.M. Bloch and O.E. Fernandez,
Hamiltonization and geometric integration of nonholonomic mechanical
systems, Proc. 8th National Congress on
Theoretical and Applied Mechanics, Brussels (Belgium) (2009), 230-236.

[pdf]

A.M. Bloch, O.E. Fernandez and T. Mestdag, Hamiltonization of nonholonomic systems and
the inverse problem of the calculus of variations,
Rep. Math. Phys. 63 (2009) 225-249.

[pdf]

M. Crampin, T. Mestdag, Reduction and reconstruction
aspects of second-order dynamical systems with symmetry. Acta Appl.
Math. (2009) 105: 241-266.

[pdf]

### 2008

O.E. Fernandez, A.M. Bloch and T. Mestdag, The Pontryagin maximum principle applied to
nonholonomic mechanics,
Proc. 47th IEEE Conference on Decision and Control, Cancun (Mexico), 2008, 4306-4311.

[pdf]

J. Vankerschaver, E. Kanso, J. E. Marsden: The motion of solid bodies in potential ﬂow with circulation: a geometric outlook. Proceedings of the 2008 ASME Dynamic Systems and Control Conference.

J. Vankerschaver, A connection-theoretic approach to the analysis of symmetries of
nonholonomic field theories.
Proc. 10th Conf. on Differential Geometry and its Applications, World
Sci. Publ., River Edge, NJ, 2008, 703-711.

[pdf]

M. Crampin, T. Mestdag, Relative equilibria of Lagrangian systems
with symmetry. J. Geom. Phys. 58 (2008) 874-887.

[pdf]

M. Crampin and T. Mestdag, The inverse problem for invariant Lagrangians on a Lie group.
J. Lie Theory 18 (2008), 471-502.

[pdf]

M. Crampin, T. Mestdag, Routh’s procedure for non-Abelian symmetry groups.
J. Math. Phys. 49 (2008), 032901 (28p).

[pdf]

T. Mestdag, M. Crampin, Invariant Lagrangians,
mechanical connections and the Lagrange-Poincaré equations. J. Phys. A:
Math. Theor. 41 (2008) 344015 (20pp).

[pdf] [journal]

B. Langerock, Conic Distributions and Accessible Sets. J. Dyn. Control Sys. Vol. 14, No. 1, January 2008, 43-70.

[pdf]

J. Vankerschaver, D. Martin de Diego, Symmetry aspects
of nonholonomic field theories. J. Phys. A: Math. Theor. 41 (2008),
035401.

[pdf][journal]

W. Sarlet, W. Vanbiervliet, Geometric characterization of driven cofactor systems. J. Phys. A: Math. Theor. 41 (2008), 042001.

[pdf]
[journal]

### 2007

T. Mestdag, M. Crampin, A connection-theoretic approach to reduction
of second-order dynamical systems with symmetry.
Proc. Appl. Math. Mech. 7 (2007), 1030605 - 1030606.

[pdf] [journal]

D. Krupka, O. Krupková, G. Prince and W. Sarlet,
Contact symmetries of the Helmholtz form.
Differential Geometry and its Applications 25 (2007) 518-542

[journal]

F. Cantrijn. M.Crampin and B. Langerock (eds.),
Differential geometric methods in mechanics and field theory, Volume in
honour of Willy Sarlet (2007), iii-154 p.

Available on request

F. Cantrijn, J. Vankerschaver, The Skinner-Rusk approach for vakonomic and nonholonomic
field theories. In: F. Cantrijn et al (eds.), Differential geometric methods in mechanics
and field theory, Volume in honour of Willy Sarlet (2007), 1-14.

[pdf]

T. Mestdag, Relative equilibria of invariant Lagrangian
systems on a Lie group, In: F. Cantrijn et al (eds.), Differential
geometric methods in mechanics and field theory, Volume in honour of
Willy Sarlet (2007), 115-129.

[pdf]

J. Vankerschaver, Euler-Poincaré reduction for discrete field theories. J. Math. Phys. 48, 032902 (2007)

[ps] [pdf]
[journal]

J. Vankerschaver, A class of nonholonomic kinematic constraints in elasticity. J. Phys. A: Math. Theor. 40, 3389-3913 (2007)

[ps] [pdf]
[journal]

W. Sarlet, A recursive scheme of first integrals of the geodesic flow of a Finsler manifold. SIGMA 3 (2007), 024, 9 pages.

[arXiv]

J. Vankerschaver, F. Cantrijn, Discrete Lagrangian field theories on Lie groupoids. J. Geom. Phys. 57, 665-689 (2007)

[ps] [pdf] [journal]

### 2006

J. E. Aldridge, G. E. Prince, W. Sarlet, G. Thompson, An
EDS approach to the inverse problem in the calculus of variations. J.
Math. Phys. 47, 103508 (2006)

[pdf] [journal]

F. Vermeire, W. Sarlet, M. Crampin, A class of recursion
operators on a tangent bundle. J. Phys. A: Math. Gen. 39, 7319-7340
(2006)

[ps] [pdf]

### 2005

J. Vankerschaver, The momentum map for nonholonomic
field theories with symmetry. Int. J. Geom. Meth. Mod. Phys. 2,
1029-1041 (2005)

[ps] [pdf]

J. Vankerschaver, F. Cantrijn, M. de León, D. Martín de
Diego, Geometric aspects of classical field theories. Rep. Math. Phys.
56, 387-411 (2005)

[ps] [pdf]

B. Langerock, Leafwise holonomy in reduction of
nonholonomic systems. Proceedings of the 9th International Conference
on Differential Geometry and Its Applications, Prague, August 30 -
September 3, 2004, 507-516 (2005)

[ps] [pdf]

T. Mestdag, A Lie algebroid approach to Lagrangian
systems with symmetry. Proceedings of the 9th International Conference
on Differential Geometry and its Applications, Prague, August 30 -
September 3, 2004, 523-535 (2005)

[ps]
[pdf]

W. Sarlet, Adjoint symmetries in non-holonomic
mechanics. Proceedings of the 9th International Conference on
Differential Geometry and its Applications, Prague, August 30 -
September 3, 2004, 537-548 (2005)

[pdf]

D. Krupka, O. Krupkova, G. Prince, W. Sarlet, Contact
symmetries and variational sequences. Proceedings of the
9th International Conference on Differential Geometry and its
Applications, Prague, August 30 - September 3, 2004, 605-615 (2005).

[ps]
[pdf]

T. Mestdag, Lagrangian reduction by stages for
non-holonomic systems in a Lie algebroid framework. J. Phys. A: Math.
Gen. 38, 10157-10179 (2005)

[pdf]

W. Sarlet, D.J. Saunders en F. Cantrijn, Adjoint
symmetries and the generation of first integrals in non-holonomic
mechanics. J. Geom. Phys. 55, 207-225 (2005).

[ps]
[pdf]

T. Mestdag, B. Langerock, A Lie algebroid framework for nonholonomic systems. J. Phys. A: Math. Gen. 38, 1097-1111 (2005).

[ps] [pdf]

### 2004

T. Mestdag, Generalized connections on affine bundles,
in: K. Tas et al. (eds.), Global Analysis and Applied Math., AIP
Conference Proc. 729 (2004), 232-239.

[ps]
[pdf]

W. Sarlet en F. Vermeire, A class of Poisson-Nijenhuis
structures on a tangent bundle, J. Phys. A.: Math. Gen., 37(24),
6319-6336 (2004)

[pdf]

B. Langerock, Leafwise holonomy of connections over a bundle map, Diff. Geom. Appl., 20(2), 125-143 (2004)

[ps]
[pdf]

### 2003

T. Mestdag and W. Sarlet, The Berwald-type
linearisation of generalised connections, J. Phys. A.: Math. Gen.,
36(29), 8049-8069 (2003)

[ps]
[pdf]

B. Langerock, Optimal control problems with variable
endpoints, Discret. Contin. Dyn. Syst., An expanded volume for the
Wilmington Meeting, May 24-27, 2002, 506-515 (2003).

[ps]
[pdf]

T. Mestdag, Generalised connections on affine Lie algebroids, Rep. Math. Phys., 51(2-3), 297-305 (2003).

[ps]
[pdf]

T. Mestdag, J. Szilasi and V. Tóth, On the geometry of generalized metrics, Publ. Math. (Debrecen), 62(3-4), 511-545 (2003)

[ps]
[pdf]

B. Langerock, Autonomous optimal control problems, Rep. Math. Phys., 51(2-3), 259-267 (2003).

[ps]
[pdf]

B. Langerock, Geometric aspects of the Maximum Principle and lifts over a bundle map, Act. Appl. Math. 77(1), 71-104 (2003).

[ps] [pdf]

B. Langerock, A connection theoretic approach to sub-Riemannian geometry, J. of Geometry and Physics, 46(3-4), 203 - 230 (2003)

[ScienceDirect]
[pdf] [ps]

### 2002

T. Mestdag, W. Sarlet and E. Martinez, Note on generalised connections and affine bundles,

J. Phys. A: Math. Gen. 35(46), 9843-9856 (2002).

[ps]

J. Cortes, S. Martinez and F. Cantrijn, Skinner-Rusk approach to
time-dependent mechanics

Phys. Lett. A 300, 250-258 (2002)

[ps]

W. Sarlet, T. Mestdag and E. Martinez, Lie algebroid structures on a class of affine bundles

J. Math. Phys. 43(11), 5654-5674 (2002)

[ps]

T. Mestdag and V. Toth, On the geometry of Randers manifolds, Rep. Math. Phys. 50(2), 167-193 (2002).

[ps]

E. Martinez, T. Mestdag and W. Sarlet, Lie algebroid
structures and Lagrangian systems on affine bundles, J. Geom. Phys.
44(1), 70-95 (2002)

[ps]

F. Cantrijn and J. Cortes, Cosymplectic reduction of
constrained systems with symmetry, Rep. Math. Phys. 49 (2/3), 167 - 182
(2002)

[ps]

M. Crampin and W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys, 43(15), 2505-2517 (2002)

[ps]

W. Sarlet, G. Thompson and G.E. Prince, The inverse
problem in the calculus of variations: the use of geometrical calculus
in Douglas’s analysis, Trans. Amer. Math. Soc. 354, 2897-2919 (2002)

[ps]

F. Cantrijn and B. Langerock, Generalized connections over a vector bundle map, Diff. Geom. Appl. 18(3), 295-317 (2002)

[ScienceDirect]
[pdf]
[ps]

B. Langerock, Connections in sub-Riemannian geometry,
Proceedings of the 8th International Conference on Differential Geometry
and Its Applications, Opava, 27-31 August 2001, Part II, Mathematical
Publications 3, Silesian University at Opava, 105-114 (2002)

[pdf]
[ps]

W. Sarlet, T. Mestdag and E. Martinez, Lagrangian
equations on affine Lie algebroids, Proceedings of the 8th
International Conference on Differential Geometry and Its Applications,
Opava, 27-31 August 2001, Part II, Mathematical Publications 3, Silesian
University at Opava, 461-472 (2002)

[ps]

F. Cantrijn, J. Cortes, M. de Leon and D. Martin de Diego, On the geometry of generalized Chaplygin
systems, Math. Proc. Camb. Phil. Soc. 132, 323-351 (2002)

[ps]

### 2001

W. Sarlet and G. Thompson, Complex second-order
differential equations and separability, Special issue "Computational
geometry for differential equations", Appl. Algebra Engrg. Comm. Comput.
11, 333-357 (2001)

[ps]

T. Mestdag and W. Sarlet, The Berwald-type connection
associated to time-dependent second-order differential equations,
Houston J. of Math. 27, 763-797 (2001)

[ps]

W. Sarlet, Different forms of seperability of second-order equations, Nonlinear Analysis 47, 6135-6146 (2001)

[ps]

B. Langerock, Nonholonomic mechanics and connections over a bundle map, J. Phys. A, 34 L609-L615 (2001)

[pdf]
[ps]

W. Sarlet and T. Mestdag, Aspects of time-dependent
second-order differential equations: Berwald-type connections, Steps in
Differential Geometry, In: Proc. Coll. Diff. Geometry (Debrecen, July
25-30, 2000), L. Kozma, P. T. Nagy and L. Tamassy (Eds.) 283-293 (2001)

[ps]

M. Crampin and W. Sarlet, A class of non-conservative
Lagrangian systems on Riemannian manifolds, J. Math. Phys. 42,
4313-4326 (2001).

[ps]

### 2000

F. Cantrijn, M. de Leon, J.C. Marrero and D. Martin de
Diego, On almost-Poisson structures in nonholonomic mechanics: II. The
time-dependent framework, Nonlinearity 13, 1379-1409 (2000)

[ps]

W. Sarlet and A. Ramos, Adjoint symmetries, separability, and volume forms, J. Math. Phys. 41, 2877-2888 (2000)

[ps]

M. Crampin, W. Sarlet and G. Thompson, Bi-differential calculi and bi-Hamiltonian systems, J. Phys. A 33, L177-L180 (2000)

[ps]

W. Sarlet and M. Crampin, Addendum to: The integrability
conditions in the inverse problem of the calculus of variations for
second-order ordinary differential equations, Acta Applicandae
Mathematicae 60, no. 3, 213-224 (2000).

[ps]

M. Crampin, W. Sarlet and G. Thompson, Bi-differential
calculi, bi-Hamiltonian systems and conformal Killing tensors, J. Phys. A
33, 8755-8770 (2000)

[ps]

### 1999

F. Cantrijn, M. de Leon and D. Martin de Diego, On
almost-Poisson structures in nonholonomic mechanics, Nonlinearity 12,
721-737 (1999)

[ps]

F. Cantrijn, M. de Leon, J.C. Marrero and D. Martín de
Diego, Reduction of constrained systems with symmetry, J. Math. Phys.
40, 795-820 (1999)

[ps]

F. Cantrijn, A. Ibort and M. de Leon, On the geometry of multisymplectic manifolds, J. Austral. Math. Soc. 66, 303-330 (1999))

[ps]

M. Crampin, G.E. Prince, W. Sarlet and G. Thompson, The
inverse problem of the calculus of variations: separable systems. Acta
Applicandae Mathematicae 57, 239-254 (1999)

[ps]

D. Saunders, F. Cantrijn and W. Sarlet, Regularity
aspects and Hamiltonization of non-holonomic systems, J. Phys. A 32,
6869-6890 (1999)

[ps]

### 1998

F. Cantrijn, M. de Leon, J.C. Marrero and D. Martín de Diego, Reduction of nonholonomic mechanical systems with symmetry, Rep. Math. Phys. 41, 279-299 (1998)

W. Sarlet, R. Sahadevan and F. Cantrijn, Symmetries, separability and volume forms, J. Math. Phys. 39, 5908-5924 (1998)

[ps]

W. Sarlet, M. Crampin and E. Martinez, The integrability
conditions in the inverse problem of the calculus of variations for
second-order ordinary differential equations, Acta Applicaendae
Mathematicae 54, 233-273 (1998)

[ps]

### 1997

W. Sarlet, Construction of adjoint symmetries for
systems of second-order and mixed first- and second-order ordinary
differential equations, Mathematical and Computer Modelling 25, 39-49
(1997)

[ps]

W. Sarlet, F. Cantrijn and D.J. Saunders, A differential geometric setting for mixed first and second-order ordinary
differential equations, J. Phys. A 30, 4031-4052 (1997)

[ps]

### 1996

F. Cantrijn, W. Sarlet, A. Vandecasteele and E.
Martínez, Complete separability of time-dependent second-order ordinary
differential equations, Acta Applicandae Mathematicae 42, 309-334
(1996)

[ps]

W. Sarlet, A direct geometrical construction of the
dynamics of non-holonomic Lagrangian systems, Extracta Mathematicae 11,
202-212 (1996)

[ps]

M. Crampin, E. Martinez and W. Sarlet, Linear
connections for systems of second-order ordinary differential equations,
Ann. Inst. H. Poincaré 65, 223-249 (1996)

[ps]

D.J. Saunders, W. Sarlet and F. Cantrijn, A geometrical framework for the study of non-holonomic Lagrangian systems: II,
J. Phys. A 29, 4265-4274 (1996)

[ps]

F. Cantrijn, L.A. Ibort and M. de Leon, Hamiltonian structures on multisymplectic manifolds, Rend. Sem. Mat. Univ.
Pol. Torino 54, 225-236 (1996)

[ps]

### 1995

W. Sarlet, F. Cantrijn and D.J. Saunders, A geometrical framework for the study of non-holonomic Lagrangian systems, J. Phys. A 28, 3253-3268 (1995)

W. Sarlet, A. Vandecasteele, F. Cantrijn and E.
Martínez, Derivations of forms along a map: the framework for
time-dependent second-order equations, Diff. Geometry and its
Applications 5, 171-203 (1995)

[ps]

### 1994

M. Crampin, W. Sarlet, E. Martinez, G.B. Byrnes and G.E. Prince, Towards a geometrical understanding of Douglas’s
solution of the inverse problem of the calculus of variations, Inverse Problems 10, 245-260 (1994)

[ps]

E. Martinez, J. F. Carinena and W. Sarlet, Geometric characterization of separable second-order differential
equations, Math. Proc. Camb. Phil. Soc. 113, 205-224 (1993)

[ps]

F. Cantrijn, Normalized momentum maps and reduction, J. Phys. A 26, 5481-5489 (1993)

W. Sarlet and E. Martinez, Symmetries of second-order differential equations and decoupling, In : Modern Group
Analysis: advanced analytical and computational methods in mathematical physics (Proc. Internat. Workshop, Acireale, October
27-31, 1992), N.H. Ibragimov, M. Torrisi and A. Valenti (Eds.) (Kluwer), 329-335 (1993)

[ps]

### 1992

E. Martinez, J.F. Carinena and W. Sarlet, Derivations of differential
forms along the tangent bundle projection, Diff. Geometry and its Applications 2, 17-43 (1992)

[ps]

F. Cantrijn, M. de Leon and E.A. Lacomba, Gradient vector fields on cosymplectic manifolds, J. Phys. A 25, 175-188 (1992)