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In this paper, a new method for determining position and orientation of a coordinate system using its image is presented. This coordinate system is a three dimensional non-orthogonal system in respect to the two dimensional and orthogonal camera coordinate system.  In real world, it’s exactly easy to select three directions on an object so that they don’t be orthogonal and on a plane. The image of this non-orthogonal coordinate system on the camera image plane is a two dimensional coordinate system. This image is obtained by a nonlinear mapping between three dimensional worlds coordinate and two dimensional image coordinate. In this paper, we review geometric relationships between a direction of a vector on the object and its image that was presented in paper [18] months ago. Then, using these relationships for three arbitrary non-orthogonal directions which are not on a plane, a system of 15 nonlinear equations is established, and by solving it, nine unknowns are extracted. Because of the importance of the sign of these unknowns to determine true lengths and angels, it’s essential to run this system of nonlinear equations in eight cases and then best answer with right signs can be extracted. The results of this theory have been examined using simulation and programs.  In paper [18] we have to select three orthogonal vectors on an object. Since world is 3D, in some cases it is exactly difficult to choose all three directions with proper length and maybe we have to choose third vector (which is in depth) with a short length and it increase errors in finding position and orientation. But in this paper we don’t limit directions to be orthogonal, so all three directions can be in proper length and it decreases the errors.

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Conventionally flight path in airplanes and unmanned air vehicles is determined with waypoints. Waypoints are points on the surface of the earth with specific latitude and longitude. For accurate crossing the waypoints at a specific time, definition of accurate guidance error parameters is essential. Guidance algorithm based on these parameters can make appropriate commands. In this article two parameters, guidance latitude and guidance longitude, based on spherical trigonometry, are defined. Indeed these parameters show guidance error in horizontal channel and longitudinal channel respect to great circles between waypoints. These parameters can be calculated in a closed form and solution of complicated integrals, which is in geodetics on an ellipsoid, do not required. Also guidance algorithms in two channel based on these parameters are designed. In horizontal channel, a PD controller and in longitudinal channel a proportional controller on the difference between desired and real velocity, are designed as guidance algorithms. Also performance of these algorithms is shown with simulation results in comparison with plane simulation.    

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In this article bubbly flow under the specified axial pressure gradient in a curved channel is studied numerically. To do so, a second order parallelized front-tracking/finite-difference method based on the projection algorithm is implemented to solve the governing equations including the full Navier-Stokes and continuity equations in the cylindrical coordinates system using a uniform staggered grid well fitted to the geometry concerned. In the absence of gravity the mid-plane parallel to the curved duct plane, which is the symmetry plane in the single fluid flow inside the curved duct, separates the bubbly flow into two different flow regions not interacting with each other. Twelve bubbles with diameters of 0.125 wall units are distributed in the equally spaced distances from each other. The numerical results obtained indicate that for the cases studied here, the bubbles reach the statistical steady state with an almost constant final orbital motion path due to the strong secondary field. Furthermore, the effects of different physical parameters such as Reynolds number, and curvature ratio on the flow field at the no slip boundary conditions, are investigated in detail.