In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension Hamilton's phase space principle in mechanics. We introduce Hamilton-d'Alembert thermodynamic by considering nonlinear nonholonomic constraints type. particular, case which given Lagrangian degenerate, construct incorporating primary v...

We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review brie‡y the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods...

This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincaré equations that naturally includes covariant Clebsch variables via multisymplectic momentum maps. In the case of diffeomorphism groups, this approach gives a new interpretation of recently derived...

I commemorate David Lewis by describing some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to Lewis’ work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible ini...

We show that the recently formulated Equivalence Principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one–dimension is sufficient to fix the Schwarzian equation [6], implies a fundamental higher dimensional Möbius invariance which in turn univocally fixes the quantum version of the Hamilton–Jacobi equation...

Larson, B.A., 1992. Principles of stochastic dynamic optimization in resource management: the continuous-time case. Agric. Econ., 7: 91-107. A wide range of problems in economics, agriculture, and natural resource management have been analyzed using continuous-time optimal control models, where the state variables change over time in a stochastic manner. Using a firm-level investment model and ...

Based on the d’Alembert-Lagrange-Poincaré variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincaré-Hamilton equations, and study a version of corresponding Poincaré-Cartan integral invariant which a...

We study the solvability of special vectorial Hamilton–Jacobi systems of the form F(Du(x))= 0 in a Sobolev space. In this paper we establish the general existence theorems for certain Dirichlet problems using suitable approximation schemes called W1,p-reduction principles that generalize the similar reduction principle for Lipschitz solutions. Our approach, to a large extent, unifies the existi...

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group ...

A general method for proving comparison principles for Hamilton-Jacobi equations on networks is introduced. It consists in constructing a vertex test function to be used in the doubling variable technique. The first important consequence is that it provides very general existence and uniqueness results for Hamilton-Jacobi equations on networks with Hamiltonians that are not convex with respect ...