Open AccessInfluence of the size of a controllable device on time-optimal rotation generated by a moving internal mass
Author(s) -
A. M. Shmatkov
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524863292-296
Subject(s) - center of mass (relativistic) , constraint (computer aided design) , point (geometry) , rotation (mathematics) , function (biology) , mathematical analysis , mathematics , solid body , added mass , physics , control theory (sociology) , classical mechanics , mechanics , geometry , control (management) , computer science , energy–momentum relation , evolutionary biology , artificial intelligence , biology , quantum mechanics , vibration
A two-dimensional time-optimal control problem with a state constraint is studied for a closed mechanical system consisting of a mass point and a solid body that interact via internal forces. It is assumed that the mass point is not allowed to move further away from the body's center of mass than a prescribed distance. A control function is found allowing the body to be turned through a given angle in a minimum time by choosing the velocity of the mass point. In the case of reaching the state constraint, the solution is constructed in explicit form via quadratures representing elliptic integrals. A numerical example of using the derived formulas is given.