Conference publications

Abstracts

XIX conference

Hamilton-Jkobi equation - a tool for mathematical modeling of objects natural

Yakovenko G.N.

Dolgoprudny, Tsiolcovskogo, 11-59? 14177

Hamilton-Jacobi equation (HJ), together with the equations of Newton, Lagrange, Hamilton, hittaker, Jacobi forms the basis of analytical mechanics. The application of equation (HJ) in the various scientific and applied fields.

1. In the finite-mechanics with complete integral (HJ) is the general solution of the Lagrange and Hamilton. Sufficiently developed methods for calculating the total integral of [1. 2].

2. The basis of perturbation theory is the equation (HJ) [1, 3].

3. In the theory of optimal control method for Hamilton-Jacobi-Bellman-Isaac is based on equations (HJ) [4, 5].

4. Equation (TH) is a bridge between "tangible" mechanics and quantum mechanics: the basis of the Schrodinger equation, Pauli, Dirac, Klein-Gordon equation, Proca. Lippmann-Schwinger equation is (TH) [6].

This work was supported by RFBR (project 10-01-00228) and AVTSP Development of scientific potential of higher education, 2009-2011. (Project 2.1.1/3604).

References.

1. FR Gantmakher Lectures in analytical mechanics. Moscow: Nauka, 1966. 300 S.

2. Yakovenko GN Short-course analysis of the dynamics - M. BINOM. Laboratory of Knowledge, 2004. - 238.

3. AI Lurie Analytical Mechanics. - Moscow: Fizmatgiz, 1961. With 824.

4. Afanasev VN Kolmanovskii VB, Nosov VR The mathematical theory of design of control systems. - 3rd ed. - M.: Higher School, 2003. 447.

5. AI Subbotin Minimax inequalities and Hamilton-Jacobi equations. - Moscow: Nauka, 1990. - 216.

6. Yaroshevsky VA Lectures on theoretical mechanics. - Moscow, MIPT, 2001.

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