Sharif Digital Repository

In this paper, the problem of Optimal Trajectory Planning for a high speed planing boat under nonlinear equality and inequality path constraints, is addressed. First, a nonlinear mathematical model of the craft's dynamic is constructed. To solve a trajectory optimization problem, we can utilize the indirect or direct methods. In the indirect methods, the maximum principle of Pontryagin is used to transform the optimal control problem into Euler-Lagrange equations, on the other hand, in the direct methods it is necessary to transcribe the optimal control problem into a nonlinear programming problem (NLP) by discretization of states and controls. The resulted NLP can be solved by... 

In this paper, we introduce a new approach to fault detection and isolation for robot manipulators. Our technique is based on using a new simplified Euler-Lagrange (EL) equation that reduces complexity of the proposed fault detection method. The proposed approach isolates the faults and is capable of handling the uncertainty in manipulator gravity vector. It is shown that the effect of uncalibrated torque sensor measurement is asymptotically rejected in the detection process. A simulation example is presented to illustrate the results. © 2009 IEEE  

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli... 

In this paper a variational framework for joint segmentation and motion estimation is employed for inspecting heart in Cine MRI sequences. A functional including Mumford-Shah segmentation and optical flow based dense motion estimation is approximated using the phase-field technique. The minimizer of the functional provides an optimum motion field and edge set by considering both spatial and temporal discontinuities. Exploiting calculus of variation principles, multiple partial differential equations associated with the Euler-Lagrange equations of the functional are extracted, first. Next, the finite element method is used to discretize the resulting PDEs for numerical solution. Several...