Related papers: Jacobi fields in nonholonomic mechanics
We show that Jacobi fields along harmonic maps between suitable spaces preserve conformality, holomorphicity, real isotropy and complex isotropy to first order; this last being one of the key tools in the proof by Lemaire and the author of…
It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such…
Recently, M. de Le\'on el al. ([8]) have developed a geometrical description of Hamilton-Jacobi theory for multisymplectic field theory. In our paper we analyse in the same spirit a special kind of field theories which are gauge field…
In order to describe the impact of different geometric structures and constraints for the dynamics of a Hamiltonian system, in this paper, for a magnetic Hamiltonian system defined by a magnetic symplectic form, we first drive precisely the…
As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
In this paper we give a geometric description of the Jacobi equations associated to a first-order Lagrangian field theory using a prolongation of the Lagrangian $L$ on a $k$-cosymplectic formulation. Moreover, using an appropriate…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
We show that any second order dynamic equation on a configuration space $X\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\to X$ of relativistic…
In this article, I demonstrate a new method to derive Jacobi metrics from Randers-Finsler metrics by introducing a more generalised approach to Hamiltonian mechanics for such spacetimes and discuss the related applications and properties. I…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
The geometric intrinsic approach to Hojman symmetry is developed and use is made of the theory of the Jacobi last multipliers to find the corresponding conserved quantity for non divergence-free vector fields. The particular cases of…
The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics.…
A new method to find first integrals of nonlinear differential equations in Jacobi-type form is presented. The basic idea of our approach is to use one-parameter perturbed motions to find well-conceived nonlocal constants that are conserved…
Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete…
Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and…
The Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and…
Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…
In this paper we discuss a general framework based on symplectic geometry for the study of second order conditions in constrained variational problems on curves. Using the notion of L-derivatives we construct Jacobi curves, which represent…