Relevant bibliographies by topics / Lagrange's method

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Lagrange's method'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Lagrange's method"

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Srinivasan, Gopala Krishna. "A Note on Lagrange's Method of Variation of Parameters." Missouri Journal of Mathematical Sciences 19, no. 1 (February 2007): 11–14. http://dx.doi.org/10.35834/mjms/1316092232.

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Peng, Hui Lian. "Modeling and Simulating of Multi-Rigid-Body System with Friction-Affected Translational Joints." Applied Mechanics and Materials 88-89 (August 2011): 250–56. http://dx.doi.org/10.4028/www.scientific.net/amm.88-89.250.

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In this paper, a modeling and simulating method is presented for the planar rigid multi-body system with friction-affected translational joints. The dynamical equations of the non-smooth system are formulated by the first kind of Lagrange's equations in Cartesian coordinate system. The normal forces are expressed by the Lagrange multipliers, and the frictional forces are characterized by Coulomb's friction law. The state transition problem of stick-slip and normal forces of bilateral constraints is solved by an improved trial-and-error method. Finally, the planar rigid multi-body system with two translational joints is considered as a illustrative application example.
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TOMITA, Masakazu. "Analysis of forward extrusion by grid method (Application of Lagrange's method of undetermined multipliers)." Transactions of the Japan Society of Mechanical Engineers Series A 52, no. 477 (1986): 1435–39. http://dx.doi.org/10.1299/kikaia.52.1435.

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Giacaglia, G. E. O., and W. Q. Lamas. "On Euler-Lagrange's Equations: A New Approach." TEMA (São Carlos) 21, no. 2 (July 22, 2020): 359. http://dx.doi.org/10.5540/tema.2020.021.02.359.

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A new formalism is proposed to study the dynamics of mechanical systems composed of N connected rigid bodies, by introducing the concept of $6N$-dimensional composed vectors. The approach is based on previous works by the authors where a complete formalism was developed by means of differential geometry, linear algebra, and dynamical systems usual concepts. This new formalism is a method for the description of mechanical systems as a whole and not as each separate part. Euler-Lagrange's Equations are easily obtained by means of this formalism.
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TOMITA, Masakazu. "Analysis of forward extrusion by the grid method. Application of Lagrange's method of undetermined multipliers." JSME international journal 30, no. 260 (1987): 242–47. http://dx.doi.org/10.1299/jsme1987.30.242.

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Prasad Mondal, Sankar, Dileep Kumar Vishwakarma, and Apu Kumar Saha. "Solution of second order linear fuzzy difference equation by Lagrange's multiplier method." Journal of Soft Computing and Applications 2016, no. 1 (2016): 11–27. http://dx.doi.org/10.5899/2016/jsca-00063.

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Ibănescu, Radu, and Cătălin Ungureanu. "Lagrange's Equations versus Bond Graph Modeling Methodology by an Example of a Mechanical System." Applied Mechanics and Materials 809-810 (November 2015): 914–19. http://dx.doi.org/10.4028/www.scientific.net/amm.809-810.914.

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The bond graph modeling method was discovered by Henry Painter in 1959 and has quickly become a wide spread method all over the modeling engineering world. The method is based on the analysis of power circulation in systems and has some indisputable advantages over other modeling methods, based in principle on mathematical aspects. The paper proposes a comparison between the bond graph method and Lagrange's equations method, by applying both methods to model a mechanical system. The bond graph model is a graphical model. There are three possibilities to exploit the bond-graph diagram. The first one consists in deducing a system of differential or algebraic-differential equations from the diagram. The second one consists in obtaining the block diagram model from the bond graph diagram, without additionally writing any equations, followed by the block diagram implementation in the appropriate software, which permits to perform simulations at once. The third one consists in implementing the bond graph diagram directly in the appropriate software, where simulations can immediately run. The advantages and the disadvantages of the methods are emphasized, but the decision about the most appropriate method is up to the modeler.
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MANOFF, S. "EINSTEIN'S THEORY OF GRAVITATION AS A LAGRANGIAN THEORY FOR TENSOR FIELDS." International Journal of Modern Physics A 13, no. 12 (May 10, 1998): 1941–67. http://dx.doi.org/10.1142/s0217751x98000846.

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Einstein's theory of gravitation (ETG) is considered as a Lagrangian theory of tensor fields over (pseudo) Riemannian spaces without torsion (Vn spaces, n=4) by means of the method of Lagrangians with covariant derivarives (MLCD). In a trivial manner Euler–Lagrange's equations as Einstein's equations are obtained. The corresponding energy–momentum tensors (EMT's) are found for the standard for the ETG Lagrangian invariant on the basis of the covariant Noether identities. The symmetric energy–momentum tensor of Hilbert appears as an element irrelevant to the whole scheme of the considered Lagrangian thoery of tensor fields over Vn spaces despite of the fact that it has some elements of the structure of the variational EMT of Euler–Lagrange. The notion of the active gravitational rest mast density is related to the variational EMT of Euler–Lagrange and on this basis to a certain extent to the EMT of Hilbert.
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Hah, Chong-Ku. "Simulation of Scooped Swing in High Bar Using Lagrange's Method : A Case Study." Journal of the Korea Contents Association 7, no. 4 (April 28, 2007): 234–40. http://dx.doi.org/10.5392/jkca.2007.7.4.234.

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Shagal, G., and S. A. Meguid. "Effect of payloads contact upon the coupled dynamic response of two cooperating robots." Robotica 14, no. 6 (November 1996): 659–65. http://dx.doi.org/10.1017/s026357470001852x.

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The coupled dynamic response of two cooperating robots handling two flexible payloads is treated using a new algorithm. In this algorithm, the dynamic equations describing the system are obtained using Lagrange's method for the rigid robot links and the finite element method for the flexible payloads. The contact between the flexible payloads is modelled using the penalty function method and a contact search algorithm is employed to identify the contact region.
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Dissertations / Theses on the topic "Lagrange's method"

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Boyle, Cameron. "A Closed-Form Dynamic Model of the Compliant Constant-Force Mechanism Using the Pseudo-Rigid-Body Model." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/53.

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A mathematical dynamic model is derived for the compliant constant-force mechanism, based on the pseudo-rigid-body model simplification of the device. The compliant constant-force mechanism is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully validated with empirical data from five separate mechanisms, comprising two configurations of compliant constant-force mechanism. The dynamic model is cast in generalized form to represent all possible configurations of compliant constant-force mechanism. Deriving the dynamic equation from the pseudo-rigid-body model is useful because every configuration is represented by the same model, so a separate treatment is not required for each configuration. An unexpected dynamic trait of the constant-force mechanism is discovered: there exists a range of frequencies for which the output force of the mechanism accords nearer to constant-force than does the output force at static levels.
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Griffith, Daniel Todd. "New methods for estimation, modeling and validation of dynamical systems using automatic differentiation." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1408.

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The main objective of this work is to demonstrate some new computational methods for estimation, optimization and modeling of dynamical systems that use automatic differentiation. Particular focus will be upon dynamical systems arising in Aerospace Engineering. Automatic differentiation is a recursive computational algorithm, which enables computation of analytically rigorous partial derivatives of any user-specified function. All associated computations occur, in the background without user intervention, as the name implies. The computational methods of this dissertation are enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate Embedding Method). OCEA has been recently developed and makes possible efficient computation and evaluation of partial derivatives with minimal user coding. The key results in this dissertation details the use of OCEA through a number of computational studies in estimation and dynamical modeling. Several prototype problems are studied in order to evaluate judicious ways to use OCEA. Additionally, new solution methods are introduced in order to ascertain the extended capability of this new computational tool. Computational tradeoffs are studied in detail by looking at a number of different applications in the areas of estimation, dynamical system modeling, and validation of solution accuracy for complex dynamical systems. The results of these computational studies provide new insights and indicate the future potential of OCEA in its further development.
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Meznik, Ivan. "On Economic Interpretation of Lagrange Multipliers." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82883.

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Nilsson, Ruben, and Simon Velander. "Simulering av mekaniska system med Lagranges metod." Thesis, KTH, Mekanik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-133459.

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Mekaniska system har länge varit av intresse för vetenskapen och vår förmåga att matematiskt beskriva dess dynamik är mycket god. Att effektivt kunna härleda de nödvändiga ekvationerna är dock inte trivialt och uttrycken som bildas är ofta icke-linjära differentialekvationer som ej leder till explicita lägesbeskrivningar av de rörliga komponenterna. Idag finns kraftfulla matematiska metoder och datorverktyg som möjliggör simulering av relativt komplicerade mekaniska system vilket denna rapport ägnats åt att undersöka med hjälp av exempelsystem. Två utvalda mekaniska systems beteenden med varierande begynnelsevillkor har undersökts med hjälp av datorsimuleringar. Det första systemet har bestått av två pendlar med en fjäder fastspänd mellan pendeländarna. Det andra systemet har bestått av en fritt rullande cylinder på horisontellt underlag med två pendlar fastspända på änden. Både konservativa och dissipativa system har modellerats. De konservativa systemens beteenden har genomgått enkel analys. Den matematiska metoden som använts är Lagranges metod [2] som utnyttjar systemets totala energi för att härleda rörelseekvationerna. Modellering, numerisk integrering, och grafisk simulering med animation har gjorts i programmet Maple, med tilläggspaketet Sophia [1]. Systemen har visualiserats framgångsrikt och analys av beteenden visade att båda systemen kan uppvisa periodiskt såväl som kaotiskt rörelsemönster beroende på energinivån i systemet.
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Greer, Neil. "The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems." Thesis, Heriot-Watt University, 2017. http://hdl.handle.net/10399/3266.

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In modern science and engineering there exist many heterogeneous problems, in which the material under consideration has non-uniform properties. For example when considering seepage under a dam, water will flow at vastly different rates through sand and stone. Mathematically this can be represented as an elliptic boundary value problem that has a large jump in coefficients between subdomains. The optimised Schwarz method and the related two-Lagrange multiplier method are non-overlapping domain decomposition methods that can be used to numerically solve such boundary value problems. These methods work by solving local Robin problems on each subdomain in parallel, which then piece together to give an approximate solution to the global boundary value problem. It is known that with a careful choice of Robin parameter the convergence of these methods can be sped up. In this thesis we first review the known results for the optimised Schwarz method, deriving optimised Robin parameters and studying the asymptotic performance of the method as the mesh parameter of the discretisation is refined and the jump in coefficients becomes large. Next we formulate the two-Lagrange multiplier method for a model two subdomain problem and show its equivalence to the optimised Schwarz method under suitable conditions. The two-Lagrange multiplier method results in a non-symmetric linear system which is usually solved with a Krylov subspace method such as GMRES. The convergence of the GMRES method can be estimated by constructing a conformal map from the exterior of the field of values of the system matrix to the interior of the unit disc. We approximate the field of values of the two-Lagrange multiplier system matrix by a rectangle and calculate optimised Robin parameters that ensure the rectangle is “well conditioned” in the sense that GMRES converges quickly. We derive convergence estimates for GMRES and consider the behaviour asymptotically as the mesh size is refined and the jump in coefficients becomes large. The final part of the thesis is concerned with the case of heterogeneous problems with many subdomains and cross points, where three or more subdomains coincide. We formulate the two-Lagrange multiplier method for such problems and consider known preconditioners that are needed to improve convergence as the number of subdomains increases. Throughout the thesis numerical experiments are performed to verify the theoretical results.
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Rees, M. D. "Moving point, particle and free-Lagrange methods." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235079.

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COUSSEMENT, GREGORY. "Equations d'euler-lagrange d'une methode d'optimisation et d'adaptation de maillages et unification avec d'autres methodes." Paris 11, 1996. http://www.theses.fr/1996PA112063.

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Cette these a pour objet de contribuer a l'evolution des techniques de construction de maillages par l'etude et la mise en uvre des equations d'euler-lagrange tridimensionnelles d'une methode variationnelle d'optimisation et d'adaptation de maillages structures par sous-domaines ainsi que par l'unification de la methode avec d'autres methodes populaires variationnelles et elliptiques. L'etude generalisee des fondements de la methode d'optimisation et d'adaptation consideree met en evidence les hypotheses utilisees initialement par jacquotte pour mesurer la deformation directe du maillage vis a vis d'un maillage de reference. L'analyse de la formulation euler-lagrange realisee pour les points situes a l'interieur et situes sur les bords des sous-domaines permet un traitement general de tous les points y compris de ceux soumis a des conditions de raccord multidomaine et/ou des conditions aux limites de nuds libres, fixes ou glissant sur des courbes ou des surfaces. Au travers de la double formulation variationnelle et euler-lagrange, l'unification avec d'autres methodes populaires montre que toutes ces methodes peuvent s'interpreter comme des procedures de construction de maillages qui minimisent une mesure de la deformation appreciee par le biais de proprietes controlant les changements de longueur, d'aire, de volume et/ou d'orthogonalite. Sur base du logiciel optim3d developpe a l'onera pour l'optimisation et l'adaptation de maillages multidomaines structures, la forme euler-lagrange du principe a ete mis en uvre avec succes. Pour permettre la construction de maillages, le systeme complexe d'equations differentielles couplees est linearise et est discretise par des differences finies. Le systeme algebrique resultant est resolu avec un procede hybride qui conjugue une technique de relaxation quasi-optimale de type gauss-seidel symetrique pour les points interieurs aux sous-domaines et une technique de relaxation de type jacobi pour les points de bords soumis aux conditions aux limites et aux raccords multi-domaines. La construction de maillages tridimensionnels pour des cas didactiques et des cas industriels complexes demontre la generalite des developpements realises ainsi que la robustesse de l'algorithme qui s'accommode de mauvaise initialisation, meme aleatoire, du maillage
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MOLINA, NORBERTO EDUARDO. "LAGRANGEAN METHOD TO SOLVE LAMINAR FLOW PERPENDICULAR TO AN INFINITE CYLINDER." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1990. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20444@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
Este trabalho tem por objetivo simular numericamente o escoamento externo de uma corrente laminar incompressível, em regime permanente, para baixos números de Reynolds, em torno de um corpo sólido de forma cilíndrica. A solução do problema em estudo, é obtida resolvendo-se as equações de conservação de massa e quantidade de movimento bi-dimensionais. O método numérico selecionado para resolver as equações de conservação é uma combinação do método lagrangeano das características, com o método de volumes finitos. Adota-se um sistema de coordenadas curvilíneas que se adapta ao corpo, definido a partir da solução do escoamento potencial em torno do cilindro. Uma vez completado o procedimento numérico, o campo de velocidades, a distribuição de pressões e a tensão cizalhante em torno do cilindro, são analisados. A determinação do coeficiente de arraste proveniente da pressão dinâmica e da tensão viscosa contra a superfície sólida do cilindro também é realizada. Os resultados locais e médios são comparados com resultados experimentais e numéricos disponíveis, apresentando boa concordância.
This work intends to simulate numerically the external flow of incompressible laminar stream at steady state for low Reynolds numbers around a cilindrical body. The solution of the present problem is obtained by means of the resolution of the equations of conservation of mass and momentum. The present numerical method to solve the equations of conservation is a combination of the lagrangian method of the characteristics, and the method of finite volumes. A curvilinear system of coordinates is selected to adapt to the body geometry. The mesh is generated based on the potential flow solution around the cylinder. Once performed the numerical computation, the velocity profile, the pressure and shear stress distribuitions around the cylinder are analysed. The determination of the drag from the data on dynamic pressure and viscosity effects around the cylinder is also done. The local and average results are compared with the experimental and numerical results available, with a reasonable agreement.
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Priestley, A. "Lagrange and characteristic Galerkin methods for evolutionary problems." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376942.

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Ware, Antony Frank. "A spectral Lagrange-Galerkin method for convection-dominated diffusion equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302896.

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Books on the topic "Lagrange's method"

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Fritts, Martin J., W. Patrick Crowley, and Harold Trease, eds. The Free-Lagrange Method. Berlin/Heidelberg: Springer-Verlag, 1985. http://dx.doi.org/10.1007/bfb0032238.

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Dynamic economics: Optimization by the Lagrange method. New York: Oxford University Press, 1997.

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Bertsekas, Dimitri P. Constrained optimization and Lagrange multiplier methods. Belmont, Mass: Athena Scientific, 1996.

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Huynh, Hung T. Accurate upwind methods for the Euler equations. [Washington, DC]: National Aeronautics and Space Administration, 1993.

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1943-, Fritts M. J., Crowley William Patrick, and Trease H. 1955-, eds. The Free-Lagrange method: Proceedings of the First International Conference on Free-Lagrange methods, held at Hilton Head Island, South Carolina, March 4-6, 1985. Berlin: Springer-Verlag, 1985.

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Trease, Harold E., Martin F. Fritts, and W. Patrick Crowley, eds. Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54960-9.

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INRIA Workshop on Numerical Methods for the Euler Equations of Fluid Dynamics (1983 Rocquencourt, Yvelines, France). Numerical methods for the Euler equations of fluid dynamics. Philadelphia: Society for Industrial and Applied Mathematics, 1985.

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Anderson, W. Kyle. Grid generation and flow solution method for Euler equations on unstructured grids. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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Toro, E. F. Some aspects of shock capturing methods for gas dynamics. Cranfield, Bedford, England: Dept. of Aerodynamics and Fluid Mechanics, College of Aeronautics, Cranfield Institute of Technology, 1991.

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Next Free-Lagrange Conference (1990 Moran, Wyo.). Advances in the Free-Lagrange method: Including contributions on adaptive gridding and the smooth particle hydrodynamics method : proceedings of the Next Free-Lagrange Conference held at Jackson Lake Lodge, Moran, Wyoming, USA, 3-7 June 1990. Berlin: Springer-Verlag, 1991.

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Book chapters on the topic "Lagrange's method"

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Dineen, Seán. "Method of Lagrange Multipliers." In Functions of Two Variables, 61–68. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-3250-1_9.

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Cvetkovski, Zdravko. "Method of Lagrange Multipliers." In Inequalities, 177–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23792-8_19.

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Postolache, Mihai. "Computational Methods in Lagrange Geometry." In Lagrange and Finsler Geometry, 163–76. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8650-4_14.

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Lions, P. L. "Lagrange Multipliers, Morses Indices and Compactness." In Variational Methods, 161–84. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4757-1080-9_11.

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Bellomo, Nicola, Bertrand Lods, Roberto Revelli, and Luca Ridolfi. "Lagrange and Sinc Collocation Interpolation Methods." In Generalized Collocation Methods, 33–56. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4610-3_2.

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Blanchard, Philippe, and Erwin Brüning. "Constrained Minimization Problems (Method of Lagrange Multipliers)." In Mathematical Methods in Physics, 403–11. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0049-9_31.

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Blanchard, Philippe, and Erwin Brüning. "Constrained Minimisation Problems (Method of Lagrange Multipliers)." In Variational Methods in Mathematical Physics, 63–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-82698-6_5.

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Blanchard, Philippe, and Erwin Brüning. "Constrained Minimization Problems (Method of Lagrange Multipliers)." In Mathematical Methods in Physics, 537–46. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14045-2_35.

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Chen, Guiqiang, Jianjun Liu, and Liqin Wang. "Color Image Sharing Method Based on Lagrange’s Interpolating Polynomial." In Health Information Science, 63–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29361-0_11.

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Kaparulin, D. S., S. L. Lyakhovich, and A. A. Sharapov. "Lagrange Anchor for Bargmann–Wigner Equations." In Geometric Methods in Physics, 119–26. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0645-9_10.

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Conference papers on the topic "Lagrange's method"

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Gao, Ruo Xing, Shu Run Tan, Leung Tsang, and Mei Song Tong. "A Nyström Method with Lagrange's Interpolation for Solving Electromagnetic Scattering by Dielectric Objects." In 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring). IEEE, 2019. http://dx.doi.org/10.1109/piers-spring46901.2019.9017672.

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Wang Zhi, Sun Shenghe, and Liu Yue. "Improving Precision of System Constants in Six-Port by Means of Lagrange's Multipliers Method." In Conference on Precision Electromagnetic Measurements. IEEE, 1988. http://dx.doi.org/10.1109/cpem.1988.671348.

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Andrei, Horia, Fanica Spinei, Paul Andrei, Ulrich L. Rohde, Marius Silaghi, and Helga Silaghi. "Evaluation of hilbert space techniques and lagrange's method for the analysis of dissipated power in DC circuits." In 2009 European Conference on Circuit Theory and Design (ECCTD 2009). IEEE, 2009. http://dx.doi.org/10.1109/ecctd.2009.5275120.

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Spryszyński, Stanisław, Louis A. Villanueva, and Gary Lymer. "Determination of the Static Equilibrium for Non-linear Systems by the Method of Virtual Work and Lagrange's Multipliers." In Non-Conference Specific Technical Papers - 2007. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2007. http://dx.doi.org/10.4271/2007-01-2133.

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Krishnamurthy, Senthil, and Raynitchka Tzoneva. "Comparative analyses of Min-Max and Max-Max price penalty factor approaches for multi criteria power system dispatch problem using Lagrange's method." In 2011 International Conference on Recent Advancements in Electrical, Electronics and Control Engineering (ICONRAEeCE). IEEE, 2011. http://dx.doi.org/10.1109/iconraeece.2011.6129758.

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Krishnamurthy, Senthil, and Raynitchka Tzoneva. "Comparative analyses of Min-Max and Max-Max price penalty factor approaches for multi criteria power system dispatch problem with valve point effect loading using Lagrange's method." In 2011 International Conference on Power and Energy Systems (ICPS). IEEE, 2011. http://dx.doi.org/10.1109/icpes.2011.6156650.

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Saljooghi, R., and M. T. Ahmadian. "Free Vibration Analysis of FGM Beams With Different Boundary Conditions Using RKPM Meshless Method." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47640.

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This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange’s method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform, natural frequencies match nicely with theoretical prediction.
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Lee, Seongsu, and Gwanggil Jeon. "Lagrange Method for Upsampling." In Advanced Science and Technology. Science & Engineering Research Support soCiety, 2015. http://dx.doi.org/10.14257/astl.2015.80.03.

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Sadeghi, Keyvan. "On the Lagrange’s Method for Floating Bodies." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92511.

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It is shown that, in the context of a linear theory, all fluid radiation actions on a floating body can be solely represented by a part of the fluid mechanical energy corresponding to the wetted surface of the body. In this regard, it is indicated that the linear radiation damping can be expressed by a fluid kinetic energy which has a bilinear form. Then from the Lagrange’s equations of motion, an equation of motion is derived that is called the conjugate Larange’s equation of motion. A variant of Hamilton’s principle is also introduced as the variational generator of the conjugate Lagrange’s equation of motion.
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Nguyen, Philip P., and Raymond J. Cipra. "Dynamic Analysis of Five-Bar Mechanisms With Torsional Springs Using Lagrange’s Equation and Kinematic Coefficients." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8621.

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Abstract This research investigates the dynamic motion of planar closed loop two-degree-of-freedom five-bar mechanisms with torsional springs. An analysis technique is presented which incorporates a combination of the Lagrange’s equation and the method of kinematic coefficients in a manner similar to the power equation to achieve improved efficiency. Using the basic mechanism vector loop, the kinematic coefficients and the point path kinematic coefficients are solved symbolically. This information is then incorporated into Lagrange’s equation to produce a formulation that yields the equations of motion. The analysis technique is then tested using a simple example that validates the hybrid Lagrange formulation. An example of a generic five-bar mechanism with a torsional spring is given to demonstrate the use of the analysis technique. The example illustrates the motion of the linkage and the effect of altering certain mechanism parameters. The study reveals that the dynamic response of certain five-bar mechanisms with torsional springs can be significantly altered through minor design changes.
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Reports on the topic "Lagrange's method"

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Cores, Debora, and R. A. Tapia. A Robust Choice of the Lagrange Multiplier in the SQP Newton Method. Fort Belvoir, VA: Defense Technical Information Center, October 1994. http://dx.doi.org/10.21236/ada444966.

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Judd, Kenneth, Lilia Maliar, Serguei Maliar, and Rafael Valero. Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain. Cambridge, MA: National Bureau of Economic Research, August 2013. http://dx.doi.org/10.3386/w19326.

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Osipov, G. S., N. S. Vashakidze, and G. V. Filippova. Fundamentals of the theory and methodology for solving extremal problems by the Lagrange method. Постулат, 2019. http://dx.doi.org/10.18411/postulat-2019-3-81.

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4

Ryan, Emily. Development and Multiscale Validation of Euler-Lagrange based Computational Methods for Modeling Cavitation within Fuel Injectors. Office of Scientific and Technical Information (OSTI), December 2019. http://dx.doi.org/10.2172/1597430.

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