• Corpus ID: 253265388

Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems

@inproceedings{Leon2022HamiltonJacobiTA,
  title={Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems},
  author={Manuel de Le'on and Manuel Lainz and Asier L'opez-Gord'on and Xavier Rivas},
  year={2022}
}
In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems following two approaches, obtaining two different Hamilton–Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reflects whether we are looking for solutions depending on this additional parameter or not… 
View PDF on arXiv
3 Citations
Background Citations
1
Methods Citations
1

3 Citations

Geometric Hamilton-Jacobi theory and integrability for nonholonomic and forced hybrid systems

. A hybrid system is a system whose dynamics are controlled by a mixture of both continuous and discrete transitions. The geometric framework for the Hamilton–Jacobi theory is developed to study this…

Symmetries, conservation and dissipation in time-dependent contact systems

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether’s theorem for non-autonomous…

Multicontact formulation for non-conservative field theories

A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and…

References

SHOWING 1-10 OF 79 REFERENCES

Discrete Hamilton–Jacobi theory for systems with external forces

A discrete version of systems with Rayleigh-type forces is introduced, the equations of motion are obtained and the equivalence is characterized, and a Hamilton-Jacobi theory for forced discrete Hamiltonian systems is developed.

A Hamilton-Jacobi theory for implicit differential systems

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of…

Implicit Contact Dynamics and Hamilton-Jacobi Theory

In this paper we propose a Hamilton-Jacobi theory for implicit contact Hamiltonian systems in two different ways. One is the understanding of implicit contact Hamiltonian dynamics as a Legendrian…

Symmetries, conservation and dissipation in time-dependent contact systems

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether’s theorem for non-autonomous…

The Hamilton–Jacobi Theory for Contact Hamiltonian Systems

The aim of this paper is to develop a Hamilton–Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton–Jacobi equation accordingly to the Hamiltonian and the…

Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems

The geometric formulation of Hamilton–Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions…

Geometric Hamilton–Jacobi theory for systems with external forces

In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples.…

Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior

Cosymplectic and contact structures for time-dependent and dissipative Hamiltonian systems

In this paper, we apply the geometric Hamilton–Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well…

Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems

A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of…
...