Academic literature on the topic 'Lagrangian equations of motion'

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Journal articles on the topic "Lagrangian equations of motion"

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Garcia-Sucre, M., U. Percoco, and L. Núñez. "An example of a general class of symmetries of Lagrangians and their equations of motion." Canadian Journal of Physics 69, no. 10 (1991): 1217–20. http://dx.doi.org/10.1139/p91-182.

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Results on symmetries of equations of motion and equivalent Lagrangians are applied to obtain constants of motion of the two-dimensional isotropic and anisotropic oscillators. We find that the anisotropic case provides the first example of a general kind of Lagrangian symmetries.
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Wang, T., and D. Kohli. "Closed and Expanded Form of Manipulator Dynamics Using Lagrangian Approach." Journal of Mechanisms, Transmissions, and Automation in Design 107, no. 2 (1985): 223–25. http://dx.doi.org/10.1115/1.3258712.

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An alternative derivation of the equations of motion of a chain of rigid bodies using Lagrangian equations of motion is presented. In an effort to reduce the complexity of the coefficients appearing in the equations of motion, a modified form of Lagrangian equations due to Silver [3] are utilized. This approach leads to a simplified form of coefficients of the equation of motion.
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Hajihashemi, Mahdi, and Ahmad Shirzad. "A generalized model for the classical relativistic spinning particle." International Journal of Modern Physics A 31, no. 07 (2016): 1650027. http://dx.doi.org/10.1142/s0217751x16500275.

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Following the Poincaré algebra, in the Hamiltonian approach, for a free spinning particle and using the Casimirs of the algebra, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the Lagrangian given in the literature. We analyze the dynamics of this generalized system in the Lagrangian formulation and show that the equations of motion support an oscillatory solution corresponding to the spinning nature of the system. Then we analyze the canonical structure of the system and present the correct gauge suitable for the spinning motion of the s
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Parsa, Kourosh. "THE LAGRANGIAN DERIVATION OF KANE’S EQUATIONS." Transactions of the Canadian Society for Mechanical Engineering 31, no. 4 (2007): 407–20. http://dx.doi.org/10.1139/tcsme-2007-0029.

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The Lagrangian approach to the development of dynamics equations for a multi-body system, constrained or otherwise, requires solving the forward kinematics of the system at velocity level in order to derive the kinetic energy of the system. The kinetic-energy expression should then be differentiated multiple times to derive the equations of motion of the system. Among these differentiations, the partial derivative of kinetic energy with respect to the system generalized coordinates is specially cumbersome. In this paper, we will derive this partial derivative using a novel kinematic relation f
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Udwadia, F. E., and R. E. Kalaba. "Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints." Journal of Applied Mechanics 68, no. 3 (2000): 462–67. http://dx.doi.org/10.1115/1.1364492.

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Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of
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Dreisigmeyer, David W., and Peter M. Young. "Nonconservative Lagrangian Mechanics: Purely Causal Equations of Motion." Foundations of Physics 45, no. 6 (2015): 661–72. http://dx.doi.org/10.1007/s10701-015-9892-7.

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YAKUBOVICH, E. I., and D. A. ZENKOVICH. "Matrix approach to Lagrangian fluid dynamics." Journal of Fluid Mechanics 443 (September 25, 2001): 167–96. http://dx.doi.org/10.1017/s0022112001005195.

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A new approach to ideal-fluid hydrodynamics based on the notion of continuous deformation of infinitesimal material elements is proposed. The matrix approach adheres to the Lagrangian (material) view of fluid motion, but instead of Lagrangian particle trajectories, it treats the Jacobi matrix of their derivatives with respect to Lagrangian variables as the fundamental quantity completely describing fluid motion.A closed set of governing matrix equations equivalent to conventional Lagrangian equations is formulated in terms of this Jacobi matrix. The equation of motion is transformed into a non
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Fogarasy, A. A., and M. R. Smith. "A unified tensor approach to the analysis of mechanical systems." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 211, no. 4 (1997): 313–22. http://dx.doi.org/10.1243/0954406971522079.

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It is shown in this paper that all methods of dynamic analysis of mechanisms used in practice can be derived from an invariant formed from the Lagrangian equation of motion. For the dynamic analysis of mechanisms subjected to kinematic constraint conditions, the Lagrangian equations of motion are far more suitable than the Newtonian approach. Since the Lagrangian equations are tensor equations, they are valid irrespective of what kind of generalized coordinates are used. This is not so, however, when the Newtonian approach is used. It is demonstrated by a simple example that a careless use of
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Burdík, Č., V. K. Pandey, and A. Reshetnyak. "BRST–BFV and BRST–BV descriptions for bosonic fields with continuous spin on R1,d−1." International Journal of Modern Physics A 35, no. 26 (2020): 2050154. http://dx.doi.org/10.1142/s0217751x20501547.

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Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a [Formula: see text]-dimensional Minkowski space–time using a metric-like formulation are constructed on the basis of a constrained BRST–BFV approach we propose. The resulting BRST–BFV equations of motion for a scalar field augmented by ghost operators contain different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded cons
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Jarabah, Ola. "Action Function Formulation for Conservative Systems with Second-Order Lagrangian." Applied Physics Research 10, no. 4 (2018): 50. http://dx.doi.org/10.5539/apr.v10n4p50.

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The Euler Lagrange equation is studied to obtain the equations of motion for conservative systems with second order Lagrangian. The solutions of these equations are substituted in the given Lagrangian. The action function is then derived by calculating the time integral of the Lagrangian. To explain the application of our formalism two examples are discussed.
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Dissertations / Theses on the topic "Lagrangian equations of motion"

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Silverberg, Jon P. "On Lagrangian meshless methods in free-surface flows." Thesis, (1.7 MB), 2005. http://edocs.nps.edu/AR/topic/theses/2005/Jan/05Jan_Silverberg.pdf.

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Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004.<br>"January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynami
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Shehadeh, Mhd Ali. "Geometrické řízení hadům podobných robotů." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417115.

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This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped
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Ormeci, Melda. "Inventory Control In A Build-To-Order Environment." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/11532.

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This dissertation consists of three independent sections: In the first part, focusing on the auto industry we look at the challenges and solution strategies of employing build-to-order (BTO) with global supply. We consider some familiar tools for managing domestic supply and exploit them for managing international supply, and propose new methods. We study frequency of supply as a way to improve performance. We study the impact of forecast accuracy, and conclude that improvements there alone may not be sufficient to obtain desired savings. Within this perspective we look at a new shipping poli
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Warren, Micah. "Special Lagrangian equations /." Thesis, Connect to this title online; UW restricted, 2008. http://hdl.handle.net/1773/5749.

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Haskins, Mark. "Constructing special Lagrangian cones /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Dhaouadi, Firas. "An augmented lagrangian approach for Euler-Korteweg type equations." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30139.

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On présente un modèle hyperbolique quasi-linéaire de premier ordre approximant les équations d'Euler-Korteweg (E-K), qui décrivent des écoulements de fluides compressibles dont l'énergie dépend du gradient de la densité. Le système E-K peut être vu comme les équations d'Euler-Lagrange d'un Lagrangien soumis à la conservation de la masse. Vu la présence du gradient de la densité dans le Lagrangien, des dérivées d'ordre élevé de la densité apparaissent dans les équations du mouvement. L'approche présentée ici permet d'obtenir un système d'équations hyperboliques qui approxime le système E-K. L'i
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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is rev
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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Thierauf, Rainer Georg. "A Lagrangian for a system of two dyons." PDXScholar, 1988. https://pdxscholar.library.pdx.edu/open_access_etds/3840.

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Maxwell's equations for the electromagnetic field are symmetrized by introducing magnetic charges into the formalism of electrodynamics. The symmetrized equations are solved for the fields and potentials of point particles. Those potentials, some of which are found to be singular along a line, are used to formulate the Lagrangian for a system of two dyons (particles with both electric and magnetic charge). The equations of motion are derived from the Lagrangian. It is shown that the dimensionality constants k and k * , which we r e introduced to define the units of the electromagnetic fields,
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Lu, Ming 1968. "A Lagrangian formulation of the Euler equations for subsonic flows /." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103268.

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This thesis presents a Lagrangian formulation of the Euler equations for subsonic flows. A special coordinate transformation is used to define the Lagrangian coordinates, namely the stream function and the Lagrangian distance, in function of the Cartesian coordinates. This Lagrangian formulation introduces two new geometry state variables, and a Lagrangian behavior parameter defining a pseudo-Lagrangian time used during the iteration procedure to obtain the solution for subsonic flows.<br>The eigenstructure and characteristics analysis for the new system of equations is based on a linear Jacob
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Books on the topic "Lagrangian equations of motion"

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Draxler, Roland R. Hybrid single-particle Lagrangian integrated trajectories (HY-SPLIT): Model description. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1988.

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Draxler, Roland R. Hybrid single-particle Lagrangian integrated trajectories (HY-SPLIT): Model description. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1988.

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Draxler, Roland R. Hybrid single-particle Lagrangian integrated trajectories (HY-SPLIT): Model description. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1988.

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Draxler, Roland R. Hybrid single-particle Lagrangian integrated trajectories (HY-SPLIT): Model description. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1988.

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Draxler, Roland R. Hybrid single-particle Lagrangian integrated trajectories (HY-SPLIT): Model description. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, 1988.

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Felici, Helene M. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows. National Aeronautics and Space Administration, 1992.

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Felici, Helene M. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows. Gas Turbine Laboratory, Massachusetts Institute of Technology, 1992.

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Zalzala, A. M. S. A distributed pipelined architecture of the recursive Lagrangian equations of motion for robot manipulators with VLSI implementation. University of Sheffield, Dept. of Control Engineering, 1989.

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Meĭrmanov, A. M. Evolution equations and Lagrangian coordinates. Walter de Gruyter, 1997.

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Bennett, Andrew F. Lagrangian fluid dynamics. Cambridge University Press, 2005.

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Book chapters on the topic "Lagrangian equations of motion"

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Stupakov, Gennady, and Gregory Penn. "The Basic Formulation of Mechanics: Lagrangian and Hamiltonian Equations of Motion." In Graduate Texts in Physics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90188-6_1.

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Shafarevich, Andrei. "Differential Equations on Polytopes: Laplacians and Lagrangian Manifolds, Corresponding to Semiclassical Motion." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01156-7_30.

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Yuan, Yu. "Special Lagrangian Equations." In Geometric Analysis. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-34953-0_21.

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Olguín Díaz, Ernesto. "Lagrangian Formulation." In 3D Motion of Rigid Bodies. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04275-2_7.

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Layton, Richard A. "Lagrangian DAEs of Motion." In Mechanical Engineering Series. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0597-5_3.

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Aldrovandi, Ruben, and José Geraldo Pereira. "Lagrangian and Field Equations." In Teleparallel Gravity. Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5143-9_9.

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Tahir-Kheli, Raza. "Oscillatory Motion." In Ordinary Differential Equations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76406-1_8.

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Colombo, Maria. "Lagrangian structure of transport equations." In Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations. Scuola Normale Superiore, 2017. http://dx.doi.org/10.1007/978-88-7642-607-0_4.

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Scherer, Philipp O. J. "Equations of Motion." In Graduate Texts in Physics. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00401-3_12.

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Diacu, Florin. "Equations of motion." In Relative Equilibria of the Curved N-Body Problem. Atlantis Press, 2012. http://dx.doi.org/10.2991/978-94-91216-68-8_3.

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Conference papers on the topic "Lagrangian equations of motion"

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Feeny, B. F. "D’Alembert’s Principle and the Equations of Motion for Nonholonomic Systems." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14533.

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D'Alembert's principle is manipulated in the presence of nonholonomic constraints to derive the principle of virtual power in nonholonomic form, and Lagrange's equations for nonholonomic systems. The Lagrangian equations had been expressed previously for conservative systems, derived by variational methods. The D'Alembert derivation confirms the roles of constrained and unconstrained Lagrangians directly by the presence of constrained and unconstrained velocities in D'Alembert's principle. The constrained form of nonconservative generalized forces is also determined for both particles and rigi
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Mahmoodi, S. Nima, Siamak E. Khadem, and Ebrahim Esmailzadeh. "Equations of Nonlinear Motion of Viscoelastic Beams." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84944.

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A viscoelastic nonlinear beam with cubic nonlinearities is considered. In order to obtain the equations of nonlinear motion of the beam for large deformation vibrations, the Lagrangian dynamics and Hamilton principle is used. It is considered that the beam vibrates in two directions, one in longitudinal direction and the other in the transverse direction. Large amplitude vibrations cause the nonlinearities in inertia and geometry terms. Also, due to viscoelastic property of the beam, a nonlinear damping term is appeared in the equations of motion. Using the condition of inextensible beams, the
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MARANDI, S., and V. MODI. "An alternate transition from the Lagrangian of a satellite to equations of motion." In Astrodynamics Conference. American Institute of Aeronautics and Astronautics, 1988. http://dx.doi.org/10.2514/6.1988-4221.

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Frye, Jason P., and Brian C. Fabien. "Control of Constrained Systems Described by Lagrangian DAEs." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47502.

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In this paper, a nonlinear controller design for constrained systems described by Lagrangian differential algebraic equations (DAEs) is presented. The controller design utilizes the structure introduced by the coordinate splitting formulation, a numerical technique used for integration of DAEs. In this structure, the Lagrange multipliers associated with the constraint equations are eliminated, and the equations of motion are transformed into implicit differential equations. Making use of this, a feedback linearizing controller can be chosen for successful motion tracking of the constrained sys
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Deshmukh, Rohan, David A. Spencer, and James Longuski. "Derivation of Atmospheric Flight Equations of Motion using Lagrangian Dynamics and its Application to Aerocapture." In AIAA Scitech 2020 Forum. American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-1742.

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Vinogradov, Oleg. "Generation of Motion Equations for a Tree-Like System of Granular Bodies." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0148.

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Abstract An arbitrary system of 3D-bodies made out of rigid spheres and arranged topologically in a tree is considered. For such a system explicit expressions for the equations of motion are derived based on the Lagrangian approach. The equations are given in terms of the path matrix characterizing the topological tree. The analytical method of generation of equations of motion makes the computer simulation of the nonsteady motion of the discrete system of bodies more efficient in term of both computer time and accuracy. It is achieved by avoiding operations with large sparse matrices (if the
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Bae, D. S., and Y. S. Won. "A Hamiltonian Equation of Motion for Realtime Vehicle Simulation." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0062.

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Abstract A relative coordinate formulation of the Hamiltonian equation of motion is derived for realtime vehicle simulation. The Baumgarte stabilization method [1] is adopted to solve the Differential-Algebraic Equations (DAE) of motion. The stability theory of multi-step integration methods is used to determine the stabilization constant. The equations of motion are first derived in Cartesian space and are reduced to relative coordinate space using the velocity transformation method [2]. Partial derivative of the kinetic energy with respect to the relative coordinate is obtained from equivale
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Gudarzi, Mohammad, Hossein Ehsani, and Mostafa Rostami. "Deriving a closed form of equations of motion of musculoskeletal system of human body: Using Lagrangian dynamics." In 2011 18th Iranian Conference of Biomedical Engineering (ICBME). IEEE, 2011. http://dx.doi.org/10.1109/icbme.2011.6168558.

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Rastogi, Vikas, Amalendu Mukherjee, and Anirvan Dasgupta. "Extended Lagrangian Formalism and Invariants of Motion of Dynamical Systems: A Case Study of Electromechanical System." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79113.

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In this paper, an extended Lagrangian formalism for general class of dynamical systems with dissipative, non-potential fields is formulated with the aim to obtain invariants of motion for such systems. A new concept of umbra-time has been introduced for this extension. D’Alembert basic idea of allowing displacement, when the real time is frozen is conveniently expressed in the terms of umbra-time. This leads to a peculiar form of equations, which is termed as umbra-Lagrange’s equations. A variational or least action doctrine leading to the proposed form of equation is introduced, which is base
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Khulief, Y. A. "Dynamic Analysis of Mechanisms Using Constrained Lagrangian Bond Graphs." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0362.

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Abstract A method for dynamic analysis of mechanisms using the Lagrangian equations of motion for an interconnected system of rigid bodies is presented. The method stems from a recent extension to the bond graph modeling technique. Intrinsically, this approach allows the formulation of the final form of equations for holonomic systems without recourse to the Lagrangian function. Consequently, the burdens of deriving the expressions for kinetic and potential energies, and performing the necessary differentiations have been eliminated. This method calls only for constructing the Jacobian matrix
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Reports on the topic "Lagrangian equations of motion"

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R.B. White, Yu.V. Yakovenko, and Ya.I. Kolesnichenko. Lagrangian Description of Nonadiabatic Particle Motion in Spherical Tori. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/798206.

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MacLachlan, J. A., and /Fermilab. Distinction between difference and differential equations of motion for synchrotron motion. Office of Scientific and Technical Information (OSTI), 2007. http://dx.doi.org/10.2172/920428.

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Courant E. D. Revised Spin Motion Equations Spin Motion and Resonances in Accelerators and Storage Rings. Office of Scientific and Technical Information (OSTI), 2008. http://dx.doi.org/10.2172/1061883.

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Parzen, G. Linear orbit parameters for the exact equations of motion. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/10126234.

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Parzen, George. Linear Orbits Parameters for the Exact Equations of Motion. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/1119381.

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Drake, JB. A Vorticity-Divergence Global Semi-Lagrangian Spectral Model for the Shallow Water Equations. Office of Scientific and Technical Information (OSTI), 2001. http://dx.doi.org/10.2172/814342.

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I.Y. Dodin, N.J. Fisch, and G.M. Fraiman. Lagrangian Formulation of Relativistic Particle Average Motion in a Laser Field of Arbitrary Intensity. Office of Scientific and Technical Information (OSTI), 2003. http://dx.doi.org/10.2172/811961.

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AIR FORCE TEST PILOT SCHOOL EDWARDS AFB CA. Volume II. Flying Qualities Phase. Chapter 4: Equations of Motion. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada319975.

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Hayek, Sabih I., and Jeffrey E. Boisvert. Equations of Motion for Nonaxisymmetric Vibrations of Prolate Spheroidal Shells. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada377034.

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Ames, Thomas L., Grant V. Farnsworth, David Isaac Ketcheson, and Allen Conrad Robinson. A comparison of Lagrangian/Eulerian approaches for tracking the kinematics of high deformation solid motion. Office of Scientific and Technical Information (OSTI), 2009. http://dx.doi.org/10.2172/984939.

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