فهرست مقالات Lagrange multipliers

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  1 - Design and Dynamic Modeling of Planar Parallel Micro-Positioning Platform Mechanism with Flexible Links Based on Euler Bernoulli Beam Theory
  N.S Viliani H Zohoor M.H Kargarnovin
  This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagran چکیده کامل

  This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane’s methods. Euler-Bernoulli beam theory is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method theory, the governing differential equations of motion are derived and solved using both Runge-Kutta-Fehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg4, 5th leads to same results. The mode frequency and the effects of geometry of flexure hinges on intermediate links vibration are investigated and the mode frequency, calculated using Fast Fourier Transform and the results are discussed. پرونده مقاله
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  2 - On the duality of quadratic minimization problems using pseudo inverses
  D. Pappas G. Domazakis
  ‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x \in \mathca چکیده کامل

  ‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x \in \mathcal{N}(H)^\perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on the strong duality principle‎, ‎we provide a closed formula for the calculation of the Lagrange multipliers $\\lambda$ in the cases when (i) the constraint equation is consistent and (ii) the constraint equation is inconsistent‎, ‎using the general normal equation‎. ‎In both cases the Moore-Penrose inverse will be used to determine a unique solution of the problems‎. ‎In addition‎, ‎in the case of a consistent constraint equation‎, ‎we also give sufficient conditions for our solution to exist using the well known KKT conditions. پرونده مقاله