The periodic motions of a gas

Two-dimensional periodic motions of a gas, described by a class of rotational and rotational-symmetrical exact solutions of the gas-dynamic equations, are considered. The investigation is based on constructing first integrals and a lemma on the existence of periodic functions, defined by quadratures of special form. The idea of limiting relations is introduced, which enable approximate relations to be established between the constituent parameters and which give a qualitative representation on the form of the periodic gas motion being investigated. In addition to examples of a limit analysis of previously known motions, an existence theorem of a new form of periodic motion called a "gaseous pinion" is presented. (C) 2001 Elsevier Science Ltd. All rights reserved.