In this problem constant and the functions are determined as follows:
where and are constants and is function
In the case the problem (I.1) - (I.3) may be a problem with a point of singularity. The solution of this problem will simplify to a singularity point and can be determined by a generalized power series.
II. The inverse problem for calculus of variations  for the problem (I.1) - (I.3) is searching a functional with Lagrangian , where the following are defined:
The equation (I.1) must be the Euler - Lagrange equation as follows
One from solutions of this problem is :
In last formula constants before argument t , variables are defined from statement of a problem.
III. Applications. The formulas (I.1) - (I.3), (II.1) have next applications: curves with a point of return (a brachistochrone, Nail parabola), a dynamics problem with variable mass (the management of a movement of the rubbish collector in the space around the earth), the problem of finding an optimal shape of a body in hypersonic flow near a point of singularity .
- Svyatskov V.A. 2000. The equation of Euler - Lagrange in boundary layer with applications. Cheboksary, Chuvash State Pedagogical University, 165 p. (in Russian).
- Svyatskov V.A. One Metod of Calculation for Optimal Shape of a Body in Hypersonic Flow near a Singular Point.//High Speed Hydrodynamics. The Intetnational Summer Scientific School. - Russia, Cheboksary: 2002. - pp. 383 - 388.
- Bronshtein I.N. and Semendyaev K.A. The Handbook on Mathematics for Engineers and Students. - M.: Nauka. - 1986. - 544 p. (in Russian).
Библиографическая ссылкаSvyatskov V.A. ABOUT ONE INVERSE PROBLEM FOR CALCULUS OF VARIATIONS AND ITS APPLICATIONS // Современные наукоемкие технологии. – 2005. – № 8. – С. 31-32;
URL: http://www.top-technologies.ru/ru/article/view?id=23450 (дата обращения: 15.06.2021).