Dynamic programming and the Hamilton-Jacobi method of classical mechanics

  • 27 Pages
  • 3.82 MB
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by
Rand Corporation , Santa Monica, Calif
Programming (Mathematics), Mechanics, Anal
StatementS.E. Dreyfus.
SeriesMemorandum -- RM-5116-PR, Memorandum (Rand Corporation) -- RM-5116-PR..
ContributionsRand Corporation.
The Physical Object
Paginationvii, 27 p. ;
ID Numbers
Open LibraryOL16648396M

Dynamic programming and the Hamilton-Jacobi method of classical mechanics (Rand Corporation. Research memorandum) [Stuart E Dreyfus] on *FREE* shipping on qualifying offers. Dynamic programming and the Hamilton-Jacobi method of classical mechanics (Memorandum) [Dreyfus, Stuart E] on *FREE* shipping on qualifying offers.

Dynamic programming and the Hamilton-Jacobi method of classical mechanics (Memorandum)Author: Stuart E Dreyfus. The conventional dynamic programming method for analytically solving a variational problem requires the determination of a particular solution, the optimal value function or return function, of the fundamental partial differential equation.

Associated with it is another function, the optimal policy function. At each point, this function yields the value of the slope of the optimal curve to Cited by: 2. Presents a new dynamic programming derivation of the classical Hamilton-Jacobi method of solving optimization problems, and develops and illustrates the connections with the usual dynamic programming approach.

31 pp. Ref. (Author. Finally, it is shown that the functional equation characterization readily yields the Hamilton-Jacobi partial differential equation of classical mechanics. DYNAMIC PROGRAMMING FORMULATION We shall consider initially the simplest problem in the Calculus of Variations.

We wish to determine the curve y connecting the points (^o'Vo) an(!Cited by: PDF | This paper presents the Hamilton-Jacobi method for integrating the equations of motion of mechanical systems on time scales.

We give the criterion | Find, read and cite all the research. The above looks a lot like the commutators of operators in quantum mechanics, such as: [x;^ p^] = i~ () Indeed, quantizing a classical theory by replacing Poisson brackets with commutators through: [u;v] = i~fu;vg () is a popular approach (rst studied by Dirac).

It is also the root of the name \canonical quantization". Buy Dynamic programming and the Hamilton-Jacobi method of Dynamic programming and the Hamilton-Jacobi method of classical mechanics book mechanics (Memorandum) by Stuart E Dreyfus (ISBN:) from Amazon's Book Store.

Everyday low prices and free delivery on eligible : Stuart E Dreyfus. Buy Dynamic programming and the Hamilton-Jacobi method of classical mechanics (Rand Corporation. Research memorandum) by Stuart E Dreyfus (ISBN:) from Amazon's Book Store.

Description Dynamic programming and the Hamilton-Jacobi method of classical mechanics FB2

Everyday low prices and free delivery on eligible : Stuart E Dreyfus. dynamic programming methods: • the intertemporal allocation problem for the representative agent in a fi-nance economy; • the Ramsey model in four different environments: • discrete time and continuous time; • deterministic and stochastic methodology • we use analytical methods • some heuristic proofs.

the properties of the new method. Key words. patchy methods, Hamilton-Jacobi equations, parallel methods, minimum time problem, semi-Lagrangian schemes. AMS subject classifications. 65N55, 49L20 1. Introduction. The numerical solution of partial differential equations ob-tained by applying the Dynamic Programming Principle (DPP) to nonlinear.

A new dynamic programming derivation is presented for the classical Hamilton-Jacobi method of solving optimization problems. The connections with the usual dynamic programming approach are developed and illustrated.

Author. In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which.

As it is well known, the Hamilton-Jacobi equation [1–4], that is an important nonlinear partial differential equation, represents a reformulation of classical mechanics. In addition, the Hamilton-Jacobi method is very useful in integrating differential equations of motion for the holonomic mechanical systems [ 5 – 9 ], the nonholonomic.

Three methods, using dynamic programming concepts and principles, for analytically solving a variational problem. The conventional dynamic programming method is described and illustrated and two alternatives to the conventional method are developed. While the derivations are new, the results are equivalent to those of the classical Hamilton-Jacobi method of solving optimization problems.

equation is a result of the theory of dynamic programming which was pioneered by Bellman. In continuous time, the result can be seen as an extension of earlier work in classical physics on the Hamilton-Jacobi equation.

The HJB equations we consider arise from optimal control models for stochastic processes. Outline In this Chapter we brie. Advances in the study of dynamical systems have revolutionized the way that classical mechanics is taught and understood.

The authors cover all the material that one would expect to find in a standard graduate course: Lagrangian and Hamiltonian dynamics, canonical transformations, the Hamilton-Jacobi equation, perturbation methods, and rigid. In this case, the equation is the well-known Hamilton-Jacobi-Bellman equation.

The problem is formulated as follows: The state equation of the control problem is a classical one. The cost function is described by an adapted solution of a certain backward stochastic differential equation. Bellman developed a dynamic programming method in [2] with his colleagues.

This so-called Hamilton-Jacobi-Bellman equation defines a broader class of equations, than the version from the classical mechanics.

Mathematicians have been working on solving this equations for many years. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way.

We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law.

PHYSCONCatania, Italy, September, 1–September, 4 DYNAMIC PROGRAMMING APPROACHES TO THE HAMILTON-JACOBI-BELLMAN THEORY OF ENERGY SYSTEMS. MECHANICS Classical Mechanics, Second Edition presents a complete account of the classical mechanics of particles and systems for physics students at the advanced undergraduate level.

The book evolved from a set of lecture notes for a course on the subject taught by the author at California State University, Stanislaus, for many years. Review: Landau & Lifshitz vol.1, Mechanics. (Typically used for the prerequisite Classical Mechanics II course and hence useful here for review) Lagrangian & Hamiltonian Mechanics Newtonian Mechanics In Newtonian mechanics, the dynamics of a system of Nparticles are determined by solving for their coordinate trajectories as a function of time.

Tree DP Example Problem: given a tree, color nodes black as many as possible without coloring two adjacent nodes Subproblems: – First, we arbitrarily decide the root node r – B v: the optimal solution for a subtree having v as the root, where we color v black – W v: the optimal solution for a subtree having v as the root, where we don’t color v – Answer is max{B.

Details Dynamic programming and the Hamilton-Jacobi method of classical mechanics PDF

Hamilton-Jacobi-Bellman equations, approximation methods, –nite and in–nite hori-zon formulations, basics of stochastic calculus. Pontryagin™s maximum principle, ODE and gradient descent methods, relationship to classical mechanics.

Linear-quadratic-Gaussian control, Riccati equations, iterative linear approximations to nonlinear. Lecture Notes on Classical Mechanics (A Work in Progress) Daniel Arovas Department of Physics University of California, San Diego May 8, In this paper we present a new algorithm for the solution of Hamilton--Jacobi--Bellman equations related to optimal control problems.

The key idea is to divide the domain of computation into subdom. This paper deals with the problem to establish a profound relationship between Pontryagin's maximum principle and Bellman 's dynamic programming method via the canonical transformations of the variables, as it is a case in classical mechanics.

A rigorous form of the Hamilton‐Jacobi theorem is proved for optimal control systems. Further it is shown that the controlled systems may be treated. equation and give an idea of the numerical methods we can use to solve this equation. A section is devoted to the technique for the comparison and stability results for Hamilton Jacobi equations.

Please note that in the bibliography we will only cite the main books on the subjects: please refer to the bibliography therein for more informations. Hamilton-Jacobi theory Novem We conclude with the crowning theorem of Hamiltonian dynamics: a proof that for any Hamiltonian.

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Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, ), classical mechanics is only a geometrical optics approximation to a wave theory!

In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of .This is a list of notable textbooks on classical mechanics and quantum mechanics arranged according to level and surnames of the authors in alphabetical order.

Contents 1 Undergraduate. Classical Mechanics, Second Edition presents a complete account of the classical mechanics of particles and systems for physics students at the advanced undergraduate level. The book evolved from a set of lecture notes for a course on the subject taught by the author at California State University, Stanislaus, for many years.

It assumes the reader has been exposed to a course in Reviews: 1.