THE ANALOGIES OF FLUID PLANE POTENTIAL FLOWS FOR DETERMINING AXIAL SYMMETRIC FLOWS OR SOLVING PROBLEMS FROM LAGRANGIAN MECHANICS

Abstract

In this paper there are presented methods for obtaining fluid axial symmetry movements or solving some problems from Lagrangian mechanics using the complex potential of plan potential movements. The first section presents two methods to determine potential axial symmetry fields knowing the complex potential in plane movement case. The two methods are based on geometry transformation, especially, making the transformations whit the help of defined operators over plane velocity field or over complex plane potential hydrodynamic. In the second section will connect the hydrodynamic plane potential and the velocities field from Lagrangian mechanics determining potential energy and trajectories. So , knowing the complex potential we will determine movements of the material point in Lagrangian mechanics and conversely.