Two models of pipeline oscillations in a gravity field are considered. The first model is based on the assumption that the horizontal displacements are absent, or they are small, as well as the first derivatives are small too. This assumption allows one to formulate the equilibrium problem in the form of a second-order differential equation. In the second model these assumptions are not available, and this leads to a system of two nonlinear ordinary second-order differential equations. The single equation and the system have the first integrals, and the corresponding boundary problem is reduced to a system of nonlinear algebraic equations. To solve it, a new method is proposed. Also dynamics of the pipeline with fluid moving inside is considered and a series of exact solutions are obtained
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