# Preprints of members of the network

*For publication details we refer to the arXiv pages.*

- D. J. Saunders, O. Rossi, G. E. Prince, Tangent bundle geometry induced by second order partial differential equations.

[arXiv:1412.2377]*This paper is related to work package 3.* - V. A. Diaz, D. Martin de Diego, Generalized variational calculus for continuous and discrete mechanical systems.

[arXiv:1411.3276]*This paper is related to work package 4.* - H. Cendra, V. A. Diaz, Lagrange-d'Alembert-Poincare equations by several stages.

[arXiv:1406.7271]*This paper is related to work package 2.* - H. Cendra, S. Capriotti, Cartan algorithm and Dirac constraints for Griffiths variational problems.

[arXiv:1309.4080]*This paper is related to work package 2.* - A. Bloch, L. Colombo, R. Gupta, D. Martin de Diego, A geometric approach to the optimal control of nonholonomic mechanical systems.

[arXiv:1410.5682]*This paper is related to work package 2.* - L. Colombo, S. Ferraro, D. Martin de Diego, Geometric integrators for higher-order variational systems and their application to optimal control.

[arXiv:1410.5766]*This paper is related to work package 4.* - F. Jimenez, H. Yoshimura, Dirac Structures in Vakonomic Mechanics.

[arXiv:1405.5394]*This paper is related to work package 1 and 2.* - C. M. Campos, M. de Leon, D. Martin de Diego, Miguel Vaquero, Hamilton-Jacobi theory in Cauchy data space.

[arXiv:1411.3959]*This paper is related to work package 1 and 2.* - M. de Leon, S. Vilarino, Lagrangian submanifolds in k-symplectic settings. Monatsh. Math. 170 (2013), no. 3-4, 381-404.

[arXiv:1202.3964]*This paper is related to work package 1.* - M. de Leon, D. Martin de Diego, M. Vaquero, A Hamilton-Jacobi theory on Poisson manifolds. J. Geom. Mech. 6 (2014), no. 1, 121-140.

[doi]*This paper is related to work package 1 and 2.* - T. Mestdag, Finsler geodesics of Lagrangian systems through Routh reduction. Mediterranean Journal of Mathematics (2015).

[arXiv:1412.3526] [doi]*This paper is related to work package 3.* - M. Barbero-Linan, M. Farre Puiggali, David Martin de Diego, Isotropic submanifolds and the inverse problem for mechanical constrained systems. J. Phys. A: Math. Theor. 48, 045210 (2015)

[arXiv:1404.1961]*This paper is related to work package 2 and 3.* - G. Waeyaert, W. Sarlet, Lifted tensors and Hamilton-Jacobi separability. J. Geom. Phys. 86 (2014), 122-133.

[arXiv:1407.4968]*This paper is related to work package 1 and 3.* - E. Garcia-Torano Andres, E. Guzman, J.C. Marrero, T. Mestdag, Reduced dynamics and Lagrangian submanifolds of symplectic manifolds. J. Phys. A: Math. Theor. 47 (2014) 225203.

[arXiv:1402.2847]*This paper is related to work package 1 and 3.* - E. Garcia-Torano Andres, B. Langerock, F. Cantrijn Aspects of reduction and transformation of Lagrangian systems with symmetry. J. Geom. Mech. 6 (2014) 1-23.

[arXiv:1402.1295]*This paper is related to work package 1.* - Z. Urban, D. Krupka, Variational theory on Grassmann fibrations: examples. Acta Math. Acad. Paed. Nyiregyhasiensis 30, No. 2 (2014).

[pdf]*This paper is related to work package 3.* - O. Rossi and D. Saunders, Dual jet bundles, Hamiltonian systems and connections. Differential Geometry and its Applications 35, Supplement, (2014), 178-198.

[pdf]*This paper is related to work package 3.* - D. Krupka, G. Moreno, Z. Urban, J. Volna, On a bicomplex induced by the variational sequence.

[pdf]*This paper is related to work package 3.* - E. Tanaka, D. Krupka, On the structure of Finsler and areal spaces. Miskolc Mathematical Notes 14, No. 2 (2013), 539-546

[arXiv:1307.1036]*This paper is related to work package 3.* - D. Krupka, Z. Urban, J. Volna, Variational projectors in fibred manifolds. Miskolc Mathematical Notes 14, No. 2 (2013), 503-516.

[pdf]*This paper is related to work package 3.* - S. Capriotti, Differential geometry, Palatini gravity and
reduction, J. Math. Phys. 55, 012902 (2014)

[doi]*This paper is related to work package 3.* - H. Cendra, M. Etchechoury and S.J. Ferraro, The Dirac Theory of Constraints, the Gotay-Nester Theory and Poisson
Geometry. Anales de la Academia Nacional de Ciencias Exactas, Fisicas y Naturales (Argentina).

[arXiv]*This paper is related to work package 1 and 2.* - H. Cendra, M. Etchechoury and S.J. Ferraro, An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems. J. Geom. Mech. 6 (2014) 167 - 236.

[arXiv:1106.3354]*This paper is related to work package 1 and 2.* - L. Colombo, M de Leon, P. Prieto Martinez, N. Roman-Roy. Unified formalism for higher-order geometric Hamilton-Jacobi theory. Int. J. Geom. Methods Mod. Phys. 11 (2014), no. 9, 1460037, 9 pp.

[arXiv:1310.1071]*This paper is related to work package 1 and 3.* - L. Colombo, M. de Leon, P. Prieto Martinez, N. Roman-Roy. Geometric Hamilton-Jacobi theory for higher-order autonomous systems. J. Phys. A 47 (2014), no. 23, 235203, 24 pp.

[arXiv:1309.2166]*This paper is related to work package 1 and 3.* - L. Colombo. Lagrange-Poincare reduction for optimal control of underactuated mechanial systems.

[arXiv:1306.6005]*This paper is related to work package 2.* - L. Colombo, P. Prieto Martinez. Unified formalism for higher-order variational problems and its applications in optimal control.
Int. J. Geom. Methods Mod. Phys. 11 (2014), no. 4, 1450034, 31 pp.

[arXiv:1304.7699]*This paper is related to work package 2 and 3.* - L. Colombo, H. Jacobs. Lagrangian mechanics on centered semi-direct product. To appear in Fields Institute Communications seires

[arXiv:1303.3883]*This paper is related to work package 3.* - L. Colombo, M. Martin de Diego, M. Zuccalli. Higher-order discrete variational problems with constraints. Journal of Mathematical Physics,Vol 54, 093507, (2013)

[doi]*This paper is related to work package 2.* - S. Ferraro, F. Jimenez, D. Martin de Diego.
New developments on the Geometric Nonholonomic Integrator.

[arXiv:1312.1587]*This paper is related to work package 4.* - J.C. Marrero, D. Martin de Diego, E. Martinez. The local description of discrete Mechanics
To appear in Fields Institute Communications seires

[arXiv:1303.4047]*This paper is related to work package 4.* - M. Barbero-Linan, M. Delgado Tellez, D. Martin de Diego. A geometric framework for discrete
Hamilton-Jacobi equation. Proceedings of Geometry and Physics: XX International Fall Workshop.
AIP Conference Proceedings.

[doi]*This paper is related to work package 4.* - M. de Leon, S. Vilarino. Hamilton-Jacobi theory in k-cosymplectic field theories.
International Journal of Geometric Methods in Modern Physics. Volume 11, Issue 01, January 2014

[doi]*This paper is related to work package 1.* - D Iglesias, JC Marrero, D. Martin de Diego, E. Padron, Disrete Dynamics in implicit form. Discret Continuous Dynamical Systems, Series A 33 - 3, pp. 1117 - 1135. 2013.

[arXiv:1011.3724]*This paper is related to work package 1 and 4.* - B Cappelletti-Montano; A De Nicola; J C Marrero; I Yudin. Examples of compact K-contact manifolds with no Sasakian metric. Int. J. Geom. Methods Mod. Phys. 11, 1460028 (2014) [10 pages].

[arXiv:1311.3270]*This paper is related to work package 1.* - L Garcia-Naranjo; J C Marrero. Non existence of an invariant measure for a homogeneous ellipsoid rolling on a plane. Reg. Chaotic Dyn. 18 - 4, pp. 372 - 379. 2013.

[arXiv:1306.4237]*This paper is related to work package 2.* - M de Leon; J C Marrero; D Martin de Diego; M Vaquero. On the Hamilton-Jacobi Theory for Singular Lagrangian Systems. J Math Phys 54, pp. 032902 - 32 pages. 2013.

[arXiv:1204.6217]*This paper is related to work package 1.* - D Iglesias; J C Marrero; M Vaquero. Poly-Poisson Structures. Lett Math Phys. 103, pp. 1103 - 1133 2013.

[arXiv:1209.4003]*This paper is related to work package 1.* - J C Marrero; N Roman Roy; M Salgado; S Vilarino. Reduction of polysymplectic manifolds. J. Phys. A: Math. Theor. 48 055206 (2015).

[arXiv:1306.0337]*This paper is related to work package 1.* - L Garcia-Naranjo; A J Maciejewski; J C Marrero; M Przybylska. The inhomogeneous Suslov problem. Physics Letters A
Volume 378, Issues 32-33, 27 (2014) 2389-2394.

[arXiv:1310.3868]*This paper is related to work package 3.* - Y Fedorov; L Garcia Naranjo; J C Marrero. Unimodularity and preservation of volumes in nonholonomic mechanics. Journal of Nonlinear Science
(2015) 25, 203-246

[arXiv:1304.1788]*This paper is related to work package 2.* - H. Bursztyn, A. Cabrera, D. Iglesias: Multisymplectic geometry and Lie groupoids, to appear in "Geometry, Mechanics and Dynamics: The Legacy of Jerry Marsden", Fields Institute Communications Series. arXiv:1312.6436 [math.SG]

[arXiv:1312.6436]*This paper is related to work package 1.* - M. Barbero-Linan, D. Iglesias Ponte, D. Martin de Diego, Morse families in optimal control problems.

[arXiv:1211.4511]*This paper is related to work package 2.* - M. de Leon, D Martin de Diego, M. Vaquero: A Universal Hamilton-Jacobi Theory, to appear in Journal of Geometric Mechanics 2014.

[arXiv:1209.5351]*This paper is related to work package 1 and 2.* - M. Barbero Linan, B. Jakubczyk, Second order conditions for optimality and local controllability of discrete-time systems. Accepted in SIAM J. Control Optim. 2014.

[arXiv:1211.5784]*This paper is related to work package 2.* - D. Iglesias-Ponte, C. Laurent-Gengoux and P. Xu, Universal lifting theorem and quasi-Poisson groupoids. J. Eur. Math. Soc. 14, Issue 3, 2012, pp. 681-731

[doi]*This paper is related to work package 1 and 3.* - W. Sarlet, G. Waeyaert, Lifting geometric objects to the dual of the first jet bundle of a bundle fibred over R. J. Geom. Phys. 74 (2013), 109-118.

[arXiv:1308.3086]*This paper is related to work package 1 and 3.* - C.M. Campos, Higher Order Variational Integrators: a polynomial approach. In: F. Casas, V. Martinez (eds.), Advances in Differential Equations and Applications. 249-258.

[arXiv:1307.6139]*This paper is related to work package 4.* - W. Sarlet, T. Mestdag, G. Prince, A generalization of Szebehely's inverse problem of dynamics. Rep. Math. Phys. 72 (2013), 65-84.

[arXiv:1305.3175]*This paper is related to work package 3.* - M. Crampin, T. Mestdag, A class of Finsler surfaces whose geodesics are circles. Publ Math. (Debrecen) 84 (1-2) (2014), 3-16.

[arXiv:1304.2965]*This paper is related to work package 3.* - O. Rossi, J. Musilova, On the inverse variational problem in nonholonomic mechanics, Commun. Math. (2012) 20, 41-62.

[pdf]*This paper is related to work package 2.* - O. Rossi, J. Musilova, The relativistic mechanics in a nonholonomic setting:
A unified approach to particles with non-zero mass and massive particles, J. Phys. A: Math. Theor. (2012) 45, 255202 (27pp).

[doi]*This paper is related to work package 2.* - O. Krupkova: Nonconservative mechanical systems with nonholonomic constraints, Sci. China: Phys. Mech. Astron. (2012) 55, 1475-1484.

[doi]*This paper is related to work package 2.* - D.J. Saunders: On null Lagrangians, accepted in Math. Slovaca.
*This paper is related to work package 3.* - D.J. Saunders, Projective metrizability in Finsler geometry, Commun. Math. (2012) 20, 63-68.

[pdf]*This paper is related to work package 3.* - I. Lacirasella, J.C. Marrero, E. Padron,
Reduction of symplectic principal R-bundles. J. Phys. A: Math. Theor. 45 (2012) 325202.

[doi]*This paper is related to work package 1.* - J.C. Marrero, M. Rodriguez Olmos, E. Padron, Reduction of symplectic-like Lie algebroids with momentum map and its application to fiberwise linear Poisson structures.
J. Phys. A: Math. Theor. 45 165201.

[doi]*This paper is related to work package 1.* - C. Martinez Campos, E. Guzman, J.C. Marrero, Classical Fields Theory of first order and Lagrangian submanifolds of premultisymplectic manifolds. J. Geom. Mech. 4, (2012) 1 - 26.

[arXiv:1009.0174]*This paper is related to work package 1.* - L. Colombo, F. Jimenez, D. Martin de Diego, Variational integrators for underactuated mechanical control systems with symmetries.

[arXiv:1209.6315]*This paper is related to work package 3 and 4.* - L. Colombo, D. Martin de Diego, On the geometry of higher-order variational problems on Lie groups. To appear in Journal Geometric Mechanics.

[arXiv:1104.3221]*This paper is related to work package 1 and 3.* - L. Colombo, F. Jimenez, D. Martin de Diego, Second-order Euler-Poincare equations for trivial principal bundles. Proceedings of the American Institue of Physics.
Geometry and Physics. 1460, 185 (2012).

*This paper is related to work package 3 and 4.* - L. Colombo, D. Martin de Diego, Optimal control of underactuated mechanical systems with symmetries. Discrete and Continuous Dynamical Systems, Supplement 2013, 149-158.
*This paper is related to work package 1 and 2.* - F. Jimenez, D. Martin de Diego, A geometric approach to discrete mechanics for optimal control theory, Proceeding of: Decision and Control (CDC), 2010 49th IEEE Conference on.
*This paper is related to work package 2.* - F. Jimenez, D. Martin de Diego, Continuous and discrete approach to vakonomic mechanics. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
March 2012,Volume 106, Issue 1, pp 75-87.

*This paper is related to work package 2.* - M. Barbero-Linan, M.C Munoz Lecanda, Presymplectic high order maximum principle. Rev. R. Acad. Cien. Serie A. Mat., March 2012, Vol. 106(1), pp 97-110.

[arXiv:1210.6773]*This paper is related to work package 2.* - M. Barbero-Linan, M.C Munoz Lecanda, K- Symplectic Pontryagin's Maximum principle for some family of PDEs. Calc. Var. Partial Differential Equations, Vol. 49, 2014, 1199-1221.

[arXiv:1210.6762]*This paper is related to work package 2.* - Y.N. Fedorov, L.C. Garcia-Naranjo, J. Vankerschaver, The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation. Disc. and Cont. Dyn. Syst. Series A 33 (2013), 4017-4040.

[arXiv:1201.5054]*This paper is related to work package 2.* - H.O. Jacobs, J. Vankerschaver, On the use of Lie groupoids in fluid-structure interactions.

[arXiv:1212.1144]*This paper is related to work package 1.* - J. Vankerschaver, M. Leok, A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects. Journal of Nonlinear Science
(2014) 24, 1-37

[arXiv:1211.4560]*This paper is related to work package 1 and 4.* - M. Barbero-Linan, M. de Leon, D. Martin de Diego,
Lagrangian submanifolds and Hamilton-Jacobi equation. Monatsh. Math., Vol. 171(3), 2013, 269-290.

[arXiv:1209.0807]*This paper is related to work package 1.* - M. de Leon, D. Martin de Diego, M. Vaquero,
A Hamilton-Jacobi Theory for Singular Lagrangian Systems in the Skinner and Rusk Setting. Int. J. Geom. Methods Mod. Phys. 9 (2012), no. 8, 1250074, 24 pp.

[arXiv:1205.0168]*This paper is related to work package 1.* - F. Jimenez, M. Kobilarov, D. Martin de Diego,
Discrete Variational Optimal Control. J. Nonlinear Sci. 23 (2013), no. 3, 393-426.

[arXiv:1203.0580]*This paper is related to work package 2 and 4.* - M. Barbero-Linan, M. de Leon, J.C. Marrero, D. Martin de Diego, M. C. Munoz-Lecanda,
Kinematic reduction and the Hamilton-Jacobi equation. J. Geom. Mech., Vol. 4(3), 2012, 207-237.

[arXiv:1110.6066]*This paper is related to work package 2.* - M. Crampin, T. Mestdag and D.J. Saunders,
Hilbert forms for a Finsler metrizable projective class of sprays. Diff. Geom. Appl. 31 (2013) 63-79.

[arXiv:1206.7021]*This paper is related to work package 3.* - B. Langerock, E. Garcia-Torano Andres, F. Cantrijn, Routh reduction and the class of magnetic Lagrangian systems. J. Math. Phys. 53, 062902 (2012).

[arXiv:1203.3302]*This paper is related to work package 3.* - M. Crampin, T. Mestdag, D. J. Saunders, The multiplier approach to the projective Finsler metrizability problem. Diff. Geom. Appl. 30 (2012), 604-621.

[arXiv:1203.3142]*This paper is related to work package 3.* - S. Capriotti, AKS systems and Lepage equivalent problems.

[arXiv:1101.1292]*This paper is related to work package 1.* - C. Martinez Campos, H. Cendra, V. Diaz, D. Martin de Diego,
Discrete Lagrange-d'Alembert-Poincare equations for Euler's disk. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
March 2012, Volume 106, Issue 1, pp 225-234.

[doi]*This paper is related to work package 4.* - S. Grillo, J.E. Marsden and S. Nair, Lyapunov constraints and global asymptotic stabilization, J. Geom. Mech 3(2), 145-196.

[doi]*This paper is related to work package 2.* - S. Capriotti, H. Montani, Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group. J. Math. Phys. 52, 073504 (2011).

[arXiv:1011.2648]*This paper is related to work package 1.* - E. Tanaka, D. Krupka, On Metrizability of Invariant Affine Connections. Internat. J. Geom. Met. Mod. Phys. 9 (2012) 1250014 (15 pages).

[arXiv:1111.3009]*This paper is related to work package 3.* - W. Sarlet, G. Prince, T. Mestdag and O. Krupkova, Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type. J. Phys. A: Math. Theor. 45 (2012) 085208 (13pp).

[arXiv:1112.0162]*This paper is related to work package 3.* - J. Vankerschaver, C. Liao, M. Leok, Generating Functionals and Lagrangian PDEs. J. Math. Phys. 54 (2013), 082901.

[arXiv:1111.0280]*This paper is related to work package 1.* - J. Vankerschaver, H. Yoshimura,
M. Leok, The Hamilton-Pontryagin Principle and Multi-Dirac
Structures for Classical Field Theories. J. Math. Phys. 53, nr. 7 (2012).

[pdf]*This paper is related to work packages 1 and 3.* - L.C. Garcia-Naranjo and J. Vankerschaver, Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation. J. Geom. Phys. 73 (2013) 56-69.

[arXiv:1109.3210]*This paper is related to work packages 1 and 2.* - M. de Leon, F. Jimenez, D. Martin de Diego, Lagrangian submanifold, hamiltonian dynamics and constrained variational calculus: continuous and discrete settings. J. Phys. A: Math. Theor. 45, 205204.

[arXiv:1108.5570]*This paper is related to work packages 1 and 4.* - L. Colombo, F. Jimenez and D. Martin de Diego: Discrete second-order Euler-Poincare equations. Applications to optimal control. International Journal of Geometric Methods in Modern Physics. Vol 9 (2012).

[arXiv:1109.4716]*This paper is related to work packages 2 and 4.* - M. Barbero Linan, Characterization of accessibility for affine connection control systems at some points with nonzero velocity. Proceedings of the IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, USA, December 12-15, 2011, 6528-6533.

[arXiv:1109.4544]*This paper is related to work package 2.* - M. Barbero Linan, A. D. Lewis, Geometric interpretations of the symmetric product in affine differential geometry. Int. J. Geom. Methods Mod. Phys. 09, 1250073 (2012) [33 pages].

[arXiv:1104.1208]*This paper is related to work packages 1 and 2.* - W. Sarlet and G. Waeyaert, Driven cofactor systems and Hamilton-Jacobi separability. J. Phys. A: Math. Theor. 45 (2012) 085206.

[arXiv:1109.4274]*This paper is related to work package 3.* - D.J. Saunders, Double structures and jets. Differential Geometry and its Applications 30 (2012), 59 - 64.

[arXiv:1108.6013]*This paper is related to work package 3.* - D.J. Saunders, Homogeneous variational problems: a minicourse. Communications in Mathematics (2011)
19, 91-128.

[arXiv:1108.6004]*This paper is related to work package 3.* - B. Langerock, T. Mestdag and J. Vankerschaver, Routh reduction by stages. Symmetry, Integrability and Geometry: Meth. Appl. (SIGMA) 7 (2011), 109, 31 pages.

[arXiv:1106.2950]*This paper is related to work package 1.* - J.C. Marrero, D. Martin de Diego, A. Stern, Symplectic groupoids and discrete constrained Lagrangian mechanics. Discrete Contin. Dyn. Syst., 35 (1), 367-397.

[arXiv:1103.6250]*This paper is related to work packages 1 and 4.* - T. Mestdag and M. Crampin, Involutive distributions and dynamical systems of second-order type. Diff. Geom. Appl. 29 (2011) 747-757.

[arXiv:1103.2935]*This paper is related to work package 3.* - J. Vankerschaver, H. Yoshimura, M. Leok, On the Geometry of Multi-Dirac Structures and Gerstenhaber Algebras. J. Geom. Phys. 61 (2011), nr. 8, pp. 1415-1425.

[arXiv:1102.2835]*This paper is related to work package 1.* - L. Colombo, D. Martin de Diego and M. Zuccalli, On variational integrators for optimal control of mechanical
control systems. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 106 (2012), no. 1, 161 - 171.

[pdf]*This paper is related to work package 4.* - M. Crampin and T. Mestdag, The Cartan form for constrained Lagrangian systems and the
nonholonomic Noether theorem. Int. J. Geom. Methods. Mod. Phys. 8 (2011) 897-923.

[arXiv:1101.3153]*This paper is related to work package 2.*