F. Cantrijn - Profile on Academia.edu (original) (raw)
Papers by F. Cantrijn
Vector fields generating analysis for classical dissipative systems
Journal of Mathematical Physics, 1982
A class of vector fiels is identified which (locally) generate first integrals of a dissipative s... more A class of vector fiels is identified which (locally) generate first integrals of a dissipative system. The structure of these vector fields and of the corresponding invariants is studied. The relationship with a previously proposed generalization of Noether’s theorem for nonconservative systems, is pointed out.
Differential Geometry and its Applications, 1991
A notion of super-Poisson structure in the category of (real) graded manifolds is presented and s... more A notion of super-Poisson structure in the category of (real) graded manifolds is presented and some of its properties are discussed. Some examples of Poisson supermanifolds are given. The structure of the cotangent supermanifold of a Lie supergroup is described and an extension of the Lie-Poisson reduction theorem for ordinary Lie groups is derived.
A multisymplectic structure on a manifold is defined by a closed differential form with zero char... more A multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior fc-forms on a manifold. For a class of multisymplectic manifolds admitting a 'Lagrangian' fibration, a general structure theorem is given which, in particular, leads to a classification of these manifolds in terms of a prescribed family of cohomology classes.
Canonical transformations and the Hamilton-Jacobi problem for general first-order systems derivable from a variational principle
ABSTRACT
Higher-order Noether symmetries and constants of the motion
Journal of Physics A General Physics
ABSTRACT
Symmetries, first integrals, and the inverse problem of Lagrangian mechanics. II
Journal of Physics A General Physics
ABSTRACT
Journal of Mathematical Physics
In order to clarify certain misconceptions in the literature, we discuss the details of the way d... more In order to clarify certain misconceptions in the literature, we discuss the details of the way determining equations for general symmetries of a Lagrangian system di er from determining equations for Noether symmetries, and establish the minimal set of extra conditions which have to be imposed in practical situations for the former to reduce to the latter. We further derive properties by which, in situations where the system is integrable through quadratic integrals in involution, the components of the corresponding Noether symmetries themselves can be used to compute the separation variables, if they exist, for the Hamilton-Jacobi equation.
Journal of Physics A General Physics
A geometrical framework is presented for modelling general systems of mixed first-and second-orde... more A geometrical framework is presented for modelling general systems of mixed first-and second-order ordinary differential equations. In contrast to our earlier work on non-holonomic systems, the first-order equations are not regarded here as a priori given constraints. Two non-linear (parametrised) connections appear in the present framework in a symmetrical way and they induce a third connection via a suitable fibred product. The space where solution curves of the given differential equations live, singles out a specific projection ρ among the many fibrations in the general picture. A large part of the paper is about the development of intrinsic tools -tensor fields and derivations -for an adapted calculus along ρ. A major issue concerns the extent to which the usual construction of a linear connection associated to second-order equations fails to work in the presence of coupled first-order equations. An application of the ensuing calculus is presented.
Journal of Physics A General Physics
A geometrical framework is presented for the treatment of a class of dynamical systems, which are... more A geometrical framework is presented for the treatment of a class of dynamical systems, which are modeled by a system of secondorder differential equations, coupled with first-order equations linear in the derivatives. Such problems in particular make their appearance in the study of Lagrangian systems with non-holonomic constraints. Among other things, we discuss the concepts of symmetry and adjoint symmetry for such systems and identify for that purpose an appropriate notion of 'dynamical covariant derivative' and 'Jacobi endomorphism'. The intrinsic tools which are being developed further allow a direct geometrical construction of the dynamics of non-holonomic systems. The vertically rolling disc is chosen as an illustrative example for the newly proposed formalism and results.
Cantrijn:“Skinner-Rusk approach to time-dependent mechanics”, Phys. Lett. A 300
Reports on Mathematical Physics, 1998
A geometric reduction procedure is presented for Lagrangian systems subjected to nonlinear nonhol... more A geometric reduction procedure is presented for Lagrangian systems subjected to nonlinear nonholonomic constraints in the presence of symmetries. Our approach is based on a geometrical method which enables one to deduce the constrained dynamics from the unconstrained one by projection.
Reports on Mathematical Physics, 2005
A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approa... more A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.
Cosymplectic reduction of constrained systems with symmetry
Reports on Mathematical Physics, 2002
ABSTRACT
Note on symmetries and invariants for second-order ordinary differential equations
Physics Letters A, 1980
ABSTRACT
First integrals versus configurational invariants and a weak form of complete integrability
Physica D: Nonlinear Phenomena, 1985
ABSTRACT
On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework
Nonlinearity, 2000
Page 1. On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework ... more Page 1. On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2000 Nonlinearity 13 1379 (http://iopscience.iop.org/0951-7715/13/4/322) ...
A new look at second-order equations and Lagrangian mechanics
Journal of Physics A: Mathematical and General, 1984
ABSTRACT
Gradient vector fields on cosymplectic manifolds
Journal of Physics A: Mathematical and General, 1992
ABSTRACT
Higher-order Noether symmetries and constants of the motion
Journal of Physics A: Mathematical and General, 1981
ABSTRACT
Pseudo-symmetries, Noether's theorem and the adjoint equation
Journal of Physics A: Mathematical and General, 1987
ABSTRACT
Vector fields generating analysis for classical dissipative systems
Journal of Mathematical Physics, 1982
A class of vector fiels is identified which (locally) generate first integrals of a dissipative s... more A class of vector fiels is identified which (locally) generate first integrals of a dissipative system. The structure of these vector fields and of the corresponding invariants is studied. The relationship with a previously proposed generalization of Noether’s theorem for nonconservative systems, is pointed out.
Differential Geometry and its Applications, 1991
A notion of super-Poisson structure in the category of (real) graded manifolds is presented and s... more A notion of super-Poisson structure in the category of (real) graded manifolds is presented and some of its properties are discussed. Some examples of Poisson supermanifolds are given. The structure of the cotangent supermanifold of a Lie supergroup is described and an extension of the Lie-Poisson reduction theorem for ordinary Lie groups is derived.
A multisymplectic structure on a manifold is defined by a closed differential form with zero char... more A multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior fc-forms on a manifold. For a class of multisymplectic manifolds admitting a 'Lagrangian' fibration, a general structure theorem is given which, in particular, leads to a classification of these manifolds in terms of a prescribed family of cohomology classes.
Canonical transformations and the Hamilton-Jacobi problem for general first-order systems derivable from a variational principle
ABSTRACT
Higher-order Noether symmetries and constants of the motion
Journal of Physics A General Physics
ABSTRACT
Symmetries, first integrals, and the inverse problem of Lagrangian mechanics. II
Journal of Physics A General Physics
ABSTRACT
Journal of Mathematical Physics
In order to clarify certain misconceptions in the literature, we discuss the details of the way d... more In order to clarify certain misconceptions in the literature, we discuss the details of the way determining equations for general symmetries of a Lagrangian system di er from determining equations for Noether symmetries, and establish the minimal set of extra conditions which have to be imposed in practical situations for the former to reduce to the latter. We further derive properties by which, in situations where the system is integrable through quadratic integrals in involution, the components of the corresponding Noether symmetries themselves can be used to compute the separation variables, if they exist, for the Hamilton-Jacobi equation.
Journal of Physics A General Physics
A geometrical framework is presented for modelling general systems of mixed first-and second-orde... more A geometrical framework is presented for modelling general systems of mixed first-and second-order ordinary differential equations. In contrast to our earlier work on non-holonomic systems, the first-order equations are not regarded here as a priori given constraints. Two non-linear (parametrised) connections appear in the present framework in a symmetrical way and they induce a third connection via a suitable fibred product. The space where solution curves of the given differential equations live, singles out a specific projection ρ among the many fibrations in the general picture. A large part of the paper is about the development of intrinsic tools -tensor fields and derivations -for an adapted calculus along ρ. A major issue concerns the extent to which the usual construction of a linear connection associated to second-order equations fails to work in the presence of coupled first-order equations. An application of the ensuing calculus is presented.
Journal of Physics A General Physics
A geometrical framework is presented for the treatment of a class of dynamical systems, which are... more A geometrical framework is presented for the treatment of a class of dynamical systems, which are modeled by a system of secondorder differential equations, coupled with first-order equations linear in the derivatives. Such problems in particular make their appearance in the study of Lagrangian systems with non-holonomic constraints. Among other things, we discuss the concepts of symmetry and adjoint symmetry for such systems and identify for that purpose an appropriate notion of 'dynamical covariant derivative' and 'Jacobi endomorphism'. The intrinsic tools which are being developed further allow a direct geometrical construction of the dynamics of non-holonomic systems. The vertically rolling disc is chosen as an illustrative example for the newly proposed formalism and results.
Cantrijn:“Skinner-Rusk approach to time-dependent mechanics”, Phys. Lett. A 300
Reports on Mathematical Physics, 1998
A geometric reduction procedure is presented for Lagrangian systems subjected to nonlinear nonhol... more A geometric reduction procedure is presented for Lagrangian systems subjected to nonlinear nonholonomic constraints in the presence of symmetries. Our approach is based on a geometrical method which enables one to deduce the constrained dynamics from the unconstrained one by projection.
Reports on Mathematical Physics, 2005
A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approa... more A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.
Cosymplectic reduction of constrained systems with symmetry
Reports on Mathematical Physics, 2002
ABSTRACT
Note on symmetries and invariants for second-order ordinary differential equations
Physics Letters A, 1980
ABSTRACT
First integrals versus configurational invariants and a weak form of complete integrability
Physica D: Nonlinear Phenomena, 1985
ABSTRACT
On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework
Nonlinearity, 2000
Page 1. On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework ... more Page 1. On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2000 Nonlinearity 13 1379 (http://iopscience.iop.org/0951-7715/13/4/322) ...
A new look at second-order equations and Lagrangian mechanics
Journal of Physics A: Mathematical and General, 1984
ABSTRACT
Gradient vector fields on cosymplectic manifolds
Journal of Physics A: Mathematical and General, 1992
ABSTRACT
Higher-order Noether symmetries and constants of the motion
Journal of Physics A: Mathematical and General, 1981
ABSTRACT
Pseudo-symmetries, Noether's theorem and the adjoint equation
Journal of Physics A: Mathematical and General, 1987
ABSTRACT