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Vakgroep Wiskunde

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

Preprints


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)