Optimal control of the rotation of a system of two bodies connected by an elastic rod
Abstract Optimal controls of the rotation of a mechanical system consisting of two rigid bodies, joined by an elastic rod, through a specified angle about an axis passing through the centre of mass of one of the bodies are constructed. The problem of the optimal control of the rotation of the system through a given angle with complete suppression of the oscillations of the elastic rod at the minimum of the energy functional of the control moment and the problem of time-optimality for a specified constraint on the energy functional of the control moment are solved.
In the oil production and thermal recovery in the application of oil and gas field, well of curves are regarded as the crooked canal(namely not only the canal has horizontal section but also vertical section), it instead the horizontal well before. Thus establishmented the new elbow well model, the solution of the model not only suitable for theoretical study but also easy to calculate in practical production. This article considered the problem of indeterminate percolation of spherical symmetry infinite domain described by the initial boundary value problem of the system of partial differential equation and obtained the point-source accurate solution when research on the problem of indeterminate percolation for double porosity medium. Abtained the accurate solution about mathematical model of line source from appling the point-source accurate solution, and applied the results to mathematical model of well of curves, obtained the integral expression of it’s accurate solution.