Related papers: Lagrangian submanifolds and Hamilton-Jacobi equati…
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the 2-body Hamilton equations, performs a canonical transformation to the orbital elements, and obtains…
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
Examples of non-standard construction of Hamiltonian structures for dynamical systems and the respective Hamilton-Jacobi (H-J) equations, without using Lagrangians, are presented. Alternative H-J equations for Euler top are explicitly…
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity…
In the paper we study the following problem: given a Hamilton-Jacobi equation where the Hamiltonian is convex with respect to the last variable, are there any optimal control problems representing it? In other words, we search for an…
The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problems arises from a calculus of variations' problem with a multicriteria Lagrangian function: through an embedding into a set-valued framework, a…
We develop a Hamilton-Jacobi theory for singular lagrangian systems in the Skinner-Rusk formalism. Comparisons with the Hamilton-Jacobi problem in the lagrangian and hamiltonian settings are discussed.
We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those equations regards the existence of a lower bound to the…
Generalizations of the Hamilton-Jacobi and Schrodinger equations for multidimensional variational problems of field theory are deduced. These generalizations are so-called variational differential equations.
We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union…
In this paper we aim at addressing the globalization problem of Hamilton-DeDonder-Weyl equations on a local $k$-symplectic framework and we introduce the notion of {\it locally conformal $k$-symplectic (l.c.k-s.) manifolds}. This formalism…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature…
A discussion of Lagrangian and Hamiltonian dynamics is presented at a level which should be suitable for advanced high school students. This is intended for those who wish to explore a version of mechanics beyond the usual Newtonian…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study…
The algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are found. The manifold admits a four-parameter…