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Relevant bibliographies by topics / Newton-Euler equations

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Academic literature on the topic 'Newton-Euler equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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Journal articles on the topic "Newton-Euler equations"

1

Bock, Hans Georg, Jürgen Gutekunst, Andreas Potschka, and María Elena Suaréz Garcés. "A Flow Perspective on Nonlinear Least-Squares Problems." Vietnam Journal of Mathematics 48, no. 4 (October 3, 2020): 987–1003. http://dx.doi.org/10.1007/s10013-020-00441-z.

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AbstractJust as the damped Newton method for the numerical solution of nonlinear algebraic problems can be interpreted as a forward Euler timestepping on the Newton flow equations, the damped Gauß–Newton method for nonlinear least squares problems is equivalent to forward Euler timestepping on the corresponding Gauß–Newton flow equations. We highlight the advantages of the Gauß–Newton flow and the Gauß–Newton method from a statistical and a numerical perspective in comparison with the Newton method, steepest descent, and the Levenberg–Marquardt method, which are respectively equivalent to Newton flow forward Euler, gradient flow forward Euler, and gradient flow backward Euler. We finally show an unconditional descent property for a generalized Gauß–Newton flow, which is linked to Krylov–Gauß–Newton methods for large-scale nonlinear least squares problems. We provide numerical results for large-scale problems: An academic generalized Rosenbrock function and a real-world bundle adjustment problem from 3D reconstruction based on 2D images.

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Shabana, A. A. "Dynamics of Flexible Bodies Using Generalized Newton-Euler Equations." Journal of Dynamic Systems, Measurement, and Control 112, no. 3 (September 1, 1990): 496–503. http://dx.doi.org/10.1115/1.2896170.

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A force acting on a rigid body produces a linear acceleration for the whole body together with an angular acceleration about its center of mass. This result is in fact Newton-Euler equations which are used as basis for developing many recursive formulations for open loop multibody systems consisting of interconnected rigid bodies. In this paper, generalized Newton-Euler equations are developed for deformable bodies that undergo large translational and rotational displacements. The configuration of the deformable body is identified using coupled sets of reference and elastic variables. The nonlinear generalized Newton-Euler equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial coordinates as well as the assumed displacement field. A set of intermediate reference frames having no mass or inertia are introduced for the convenience of defining various joints between interconnected deformable bodies. The use of the obtained generalized Newton-Euler equations for developing recursive dynamic formulation for open loop deformable multibody systems containing revolute, prismatic and cylindrical joints is also discussed. The development presented in this paper demonstrates the complexities of the formulation and the difficulties encountered when the equations of motion are defined in the joint coordinate systems.

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Bascetta, Luca, Gianni Ferretti, and Bruno Scaglioni. "Closed form Newton–Euler dynamic model of flexible manipulators." Robotica 35, no. 5 (November 17, 2015): 1006–30. http://dx.doi.org/10.1017/s0263574715000934.

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SUMMARYIn this paper, a closed-form dynamic model of flexible manipulators is developed, based on the Newton–Euler formulation of motion equations of flexible links and on the adoption of the spatial vector notation. The proposed model accounts for two main innovations with respect to the state of the art: it is obtained in closed form with respect to the joints and modal coordinates (including the quadratic velocity terms) and motion equations of the whole manipulator can be computed for any arbitrary shape of the links and any possible link cardinality starting from the output of several commercial (finite element analysis) FEA codes. The Newton–Euler formulation of motion equations in terms of the joint and elastic variables greatly improves the simulation performances and makes the model suitable for real-time control and active vibration damping. The model has been compared with literature benchmarks obtained by the classical multibody approach and further validated by comparison with experiments collected on an experimental manipulator.

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Xu, Xiang-Rong, Won-Jee Chung, Young-Hyu Choi, and Xiang-Feng Ma. "A new dynamic formulation for robot manipulators containing closed kinematic chains." Robotica 17, no. 3 (May 1999): 261–67. http://dx.doi.org/10.1017/s0263574799001320.

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This paper presents a new recursive algorithm of robot dynamics based on the Kane's dynamic equations and Newton-Euler formulations. Differing from Kane's work, the algorithm is general-purpose and can be easily realized on computers. It is suited not only for robots with all rotary joints but also for robots with some prismatic joints. Formulations of the algorithm keep the recurrence characteristics of the Newton-Euler formulations, but possess stronger physical significance. Unlike the conventional algorithms, such as the Lagrange and Newton-Euler algorithm, etc., the algorithm can be used to deal with dynamics of robots containing closed chains without cutting the closed chains open. In addition, this paper makes a comparison between the algorithm and those conventional algorithms from the number of multiplications and additions.

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Hwang, Yunn-Lin, and Van-Thuan Truong. "Dynamic Analysis and Control of Multi-Body Manufacturing Systems Based on Newton–Euler Formulation." International Journal of Computational Methods 12, no. 02 (March 2015): 1550007. http://dx.doi.org/10.1142/s0219876215500073.

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This paper presents the numerical dynamic analysis and control of multi-body manufacturing systems based on Newton–Euler formulation. The models of systems built with dynamical parameters are executed. The research uses Newton–Euler formulation application in mechanics calculations, where relations between contiguous bodies through joints as well as their constrained equations are considered. The kinematics and dynamics are both analyzed and acquired by practical applications. Numerical tools help to determine all dynamic characteristics of multi-body manufacturing systems such as displacements, velocities, accelerations and reaction forces of bodies and joints. Using the acquisition, the dynamic approach of multi-body manufacturing systems is developed then whole fundamentals for controller tuning are obtained. It leads to an effective solution for mechanical manufacturing system investigation. Numerical examples are also presented as the illustrations in this paper. The numerical results imply that numerical equations based on Newton–Euler algorithm are valuable in multi-body manufacturing system. It is an effective approach for solving whole mechatronic manufacturing systems including structures, kinematics, dynamics and control.

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Whittlesey, Saunders N., and Joseph Hamill. "An Alternative Model of the Lower Extremity during Locomotion." Journal of Applied Biomechanics 12, no. 2 (May 1996): 269–79. http://dx.doi.org/10.1123/jab.12.2.269.

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An alternative to the Iterative Newton-Euler or linked segment model was developed to compute lower extremity joint moments using the mechanics of the double pendulum. The double pendulum model equations were applied to both the swing and stance phases of locomotion. Both the Iterative Newton-Euler and double pendulum models computed virtually identical joint moment data over the entire stride cycle. The double pendulum equations, however, also included terms for other mechanical factors acting on limb segments, namely hip acceleration and segment angular velocities and accelerations Thus, the exact manners in which the lower extremity segments interacted with each other could be quantified throughout the gait cycle. The linear acceleration of the hip and the angular acceleration of the thigh played comparable roles to muscular actions during both swing and stance.

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Gupta, S., and M. A. Townsend. "On the Equations of Motion for Robot Arms and Open Kinematic Chains." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 3 (September 1, 1988): 287–94. http://dx.doi.org/10.1115/1.3267460.

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The closed-form equations of motion for robot arms and other open kinematic chains are derived using the Newton-Euler equations in a form particularly suitable for the automatic modeling and on-line control of such mechanisms. The approach is based on Vukobratovic’s method [3], using more conventional Western notation.

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Huang, Y., and C. S. G. Lee. "Generalization of Newton-Euler Formulation of Dynamic Equations to Nonrigid Manipulators." Journal of Dynamic Systems, Measurement, and Control 110, no. 3 (September 1, 1988): 308–15. http://dx.doi.org/10.1115/1.3152687.

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A recursive lumped mass/spring approximation model, based on the Newton-Euler formulation, is proposed to model the dynamics of manipulators with link flexibility. The model assumes that the displacement and rotation due to the link flexibility are measurable. For a small link deformation, a first-order lumped mass/spring approximation model is proposed, in which the parameters of each link are lumped to its joint and the link flexibility is modeled as a spring at each joint. For a larger deformation, the first-order lumped mass/spring approximation model is extended to model each nonrigid link by a series of small rigid segments connected by “pseudo-joints.” The link flexibility is modeled as a spring in each pseudo-joint. In both cases, the effects of torsion and extension are not included in the modeling. An anlaytical error analysis is performed to justify the approximation, and the mathematical relation between the maximum modeling error and the number of pseudo-joints in each link is derived. As the number of pseudo-joints approaches infinity, the joint torques computed by the extended lumped mass/spring approximation model approach the joint torques computed by other models obtained from the Lagrange’s equation.

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Carrillo, José A., and Young-Pil Choi. "Mean-Field Limits: From Particle Descriptions to Macroscopic Equations." Archive for Rational Mechanics and Analysis 241, no. 3 (June 1, 2021): 1529–73. http://dx.doi.org/10.1007/s00205-021-01676-x.

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AbstractWe rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.

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Xie, Shunqiang. "Kinematic analysis and Newton-Euler equations of a novel hybrid machine tool." Chinese Journal of Mechanical Engineering (English Edition) 15, supp (2002): 132. http://dx.doi.org/10.3901/cjme.2002.supp.132.

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Dissertations / Theses on the topic "Newton-Euler equations"

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Wehner, Edward. "A Newton-Krylov solver for the Euler equations on unstructured grids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ62898.pdf.

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Pueyo, Alberto. "An efficient Newton-Krylov method for the Euler and Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq35288.pdf.

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Onur, Omer. "Effect Of Jacobian Evaluation On Direct Solutions Of The Euler Equations." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf.

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A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton&
#8217
s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time. In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.

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El, Azzouzi Khalid. "Modélisation et simulation numérique à l’échelle des fibres du comportement dynamique d’un multifilament unidirectionnel en placement de fibres robotisé." Thesis, Ecole centrale de Nantes, 2016. http://www.theses.fr/2016ECDN0027.

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Le comportement mécanique d’un fil de carbone en compression transverse est caractérisé par des déplacements relatifs importants entre fibres, ce qui lui confère un comportement fortement non-linéaire lié aux contacts inter-fibres. Le caractère multi-échelle de la structure fibreuse rend problématique la caractérisation du comportement mécanique du fil de carbone utilisé dans le procédé de placement de fibres sèches automatisé. La complexité de la modélisation mécanique de ce milieu fibreux à l’échelle des fibres est due au fait que la forte non-linéarité mécanique dépend en grande partie de la configuration géométrique des fibres, des interactions de contact-frottement entre elles et le contexte dynamique de la dépose. Le couplage fort entre chargements et modes de déformation dans les différentes directions et l’évolution de la microstructure, qu’il est bien difficile d’appréhender, accentuent fortement la complexité de la modélisation d’une telle structure fibreuse. Le travail de la thèse s’inscrit dans le cadre de l’optimisation du moyen de dépose robotisé de fils secs avec une source de chaleur par laser. Afin de comprendre le comportement thermo-mécanique du fil au cours de la dépose, un modèle dynamique a été développé pour simuler un milieu fibreux en interaction. Le but est de pouvoir prédire le réarrangement des fibres dans un fil sous sollicitation, ainsi que l’évolution des points de contact entre fibres. Ce travail est une première étape vers l’objectif final qui est de définir les paramètres procédés par rapport à la nature des fils secs déposés permettant d’obtenir une préforme de bonne qualité avec une vitesse de dépose élevée
The mechanical behavior of the carbon tow in lateral pressure characterized by the relative movement between fibers giving it a non-linear behavior because of the contact inter-fibers. The fact that the fibrous structure of the tow makes it difficult to characterize its mechanical behavior during the automated placement. The complexity of the mechanical modeling of this fibrous media at fiber scale is due to the fact that the mechanical non-linearity depends in large part to the geometric configuration of fibers, the friction between fibers and also the dynamic environment of the placement. The mechanical modeling complexity is a consequence of the tight coupling between loading and deformation directions modifying the microstructure. This thesis is in keeping with the parameter optimization of the Automated Dry Fiber Placement process with a laser heat source. In order to improve understanding the thermos-mechanical behavior of tow during placement, a dynamic model has been developed to simulate the interaction between fibers. The aim is to be able to predict the geometric configuration of fibers under loading, as well as the position of the contact points. These works are the first step to achieving the objective of identifying and optimizing process parameters in order to increase the lay down speed as well as the quality of the preform

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Benyo, Krisztian. "Analyse mathématique de l’interaction d’un fluide non-visqueux avec des structures immergées." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0156/document.

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Cette thèse porte sur l’analyse mathématique de l’interaction d’un fluide non-visqueux avec des structures immergées. Plus précisément, elle est structurée autour de deux axes principaux. L’un d’eux est l’analyse asymptotique du mouvement d’une particule infinitésimale en milieu liquide. L’autre concerne l’interaction entre des vagues et une structure immergée. La première partie de la thèse repose sur l’analyse mathématique d’un système d’équations différentielles ordinaires non-linéaires d’ordre 2 modélisant le mouvement d’un solide infiniment petit dans un fluide incompressible en 2D. Les inconnues du modèle décrivent la position du solide, c’est-à-dire la position du centre de masse et son angle de rotation. Les équations proviennent de la deuxième loi de Newton avec un prototype de force de type Kutta-Joukowski. Plus précisément, nous étudions la dynamique de ce système lorsque l’inertie du solide tend vers 0. Les principaux outils utilisés sont des développements asymptotiques multiéchelles en temps. Pour la dynamique de la position du centre de masse, l’étude met en évidence des analogies avec le mouvement d’une particule chargée dans un champ électromagnétique et la théorie du centre-guide. En l’occurrence, le mouvement du centreguide est donné par une équation de point-vortex. La dynamique de l’angle est quant à elle donnée par une équation de pendule non-linéaire lentement modulée. Des régimes très différents se distinguent selon les données initiales. Pour de petites vitesses angulaires initiales la méthode de Poincaré-Lindstedt fait apparaitre une modulation des oscillations rapides, alors que pour de grandes vitesses angulaires initiales, un movement giratoire bien plus irrégulier est observé. C’est une conséquence particulière et assez spectaculaire de l’enchevêtrement des trajectoires homocliniques. La deuxième partie de la thèse porte sur le problème des vagues dans le cas où le domaine occupé par le fluide est à surface libre et avec un fond plat sur lequel un objet solide se translate horizontalement sous l’effet des forces de pression du fluide. Nous avons étudié deux systèmes asymptotiques qui décrivent le cas d’un fluide parfait incompressible en faible profondeur. Ceux-ci correspondent respectivement aux équations de Saint-Venant et de Boussinesq. Grâce à leur caractère bien-posé en temps long, les modèles traités permettent de prendre en compte certains effets de la mécanique du solide, comme les forces de friction, ainsi que les effets non-hydrostatiques. Notre analyse théorique a été complétée par des études numériques. Nous avons développé un schéma de différences finies d’ordre élevé et nous l’avons adapté à ce problème couplé afin de mettre en évidence les effets d’un solide (dont le mouvement est limité à des translations sur le fond) sur les vagues qui passent au dessus de lui. A la suite de ces travaux, nous avons souligné l’influence des forces de friction sur ce genre de systèmes couplés ainsi que sur le déferlement des vagues. Quant à l’amortissement dû aux effets hydrodynamiques, une vague ressemblance avec le phénomène de l’eau morte est mise en évidence
This PhD thesis concerns the mathematical analysis of the interaction of an inviscid fluid with immersed structures. More precisely it revolves around two main problems: one of them is the asymptotic analysis of an infinitesimal immersed particle, the other one being the interaction of water waves with a submerged solid object. Concerning the first problem, we studied a system of second order non-linear ODEs, serving as a toy model for the motion of a rigid body immersed in a two-dimensional perfect fluid. The unknowns of the model describe the position of the object, that is the position of its center of mass and the angle of rotation; the equations arise from Newton’s second law with the consideration of a Kutta-Joukowski type lift force. It concerns the detailed analysis of the dynamic of this system when the solid inertia tends to 0. For the evolution of the position of the solid’s center of mass, the study highlights similarities with the motion of a charged particle in an electromagnetic field and the wellknown “guiding center approximation”; it turns out that the motion of the corresponding guiding center is given by a point-vortex equation. As for the angular equation, its evolution is given by a slowly-in-time modulated non-linear pendulum equation. Based on the initial values of the system one can distinguish qualitatively different regimes: for small angular velocities, by the Poincaré-Lindstedt method one observes a modulation in the fast time-scale oscillatory terms, for larger angular velocities however erratic rotational motion is observed, a consequence of Melnikov’s observations on the presence of a homoclinic tangle. About the other problem, the Cauchy problem for the water waves equations is considered in a fluid domain which has a free surface on the upper vertical limit and a flat bottom on which a solid object moves horizontally, its motion determined by the pressure forces exerted by the fluid. Two shallow water asymptotic regimes are detailed, well-posedness results are obtained for both the Saint-Venant and the Boussinesq system coupled with Newton’s equation characterizing the solid motion. Using the particular structure of the coupling terms one is able to go beyond the standard scale for the existence time of solutions to the Boussinesq system with a moving bottom. An extended numerical study has also been carried out for the latter system. A high order finite difference scheme is developed, extending the convergence ratio of previous, staggered grid based models. The discretized solid mechanics are adapted to represent important features of the original model, such as the dissipation due to the friction term. We observed qualitative differences for the transformation of a passing wave over a moving solid object as compared to an immobile one. The movement of the solid not only influences wave attenuation but it affects the shoaling process as well as the wave breaking. The importance of the coefficient of friction is also highlighted, influencing qualitative and quantitative properties of the coupled system. Furthermore, we showed the hydrodynamic damping effects of the waves on the solid motion, reminiscent of the so-called dead water phenomenon

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Basu-Mandal, Pradipta. "Studies On The Dynamics And Stability Of Bicycles." Thesis, 2007. http://hdl.handle.net/2005/387.

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This thesis studies the dynamics and stability of some bicycles. The dynamics of idealized bicycles is of interest due to complexities associated with the behaviour of this seemingly simple machine. It is also useful as it can be a starting point for analysis of more complicated systems, such as motorcycles with suspensions, frame ﬂexibility and thick tyres. Finally, accurate and reliable analyses of bicycles can provide benchmarks for checking the correctness of general multibody dynamics codes. The ﬁrst part of the thesis deals with the derivation of fully nonlinear diﬀerential equations of motion for a bicycle. Lagrange’s equations are derived along with the constraint equations in an algorithmic way using computer algebra.Then equivalent equations are obtained numerically using a Newton-Euler formulation. The Newton-Euler formulation is less straightforward than the Lagrangian one and it requires the solution of a bigger system of linear equations in the unknowns. However, it is computationally faster because it has been implemented numerically, unlike Lagrange’s equations which involve long analytical expressions that need to be transferred to a numerical computing environment before being integrated. The two sets of equations are validated against each other using consistent initial conditions. The match obtained is, expectedly, very accurate. The second part of the thesis discusses the linearization of the full nonlinear equations of motion. Lagrange’s equations have been used.The equations are linearized and the corresponding eigenvalue problem studied. The eigenvalues are plotted as functions of the forward speed ν of the bicycle. Several eigenmodes, like weave, capsize, and a stable mode called caster, have been identiﬁed along with the speed intervals where they are dominant. The results obtained, for certain parameter values, are in complete numerical agreement with those obtained by other independent researchers, and further validate the equations of motion. The bicycle with these parameters is called the benchmark bicycle. The third part of the thesis makes a detailed and comprehensive study of hands-free circular motions of the benchmark bicycle. Various one-parameter families of circular motions have been identiﬁed. Three distinct families exist: (1)A handlebar-forward family, starting from capsize bifurcation oﬀ straight-line motion, and ending in an unstable static equilibrium with the frame perfectly upright, and the front wheel almost perpendicular. (2) A handlebar-reversed family, starting again from capsize bifurcation, but ending with the front wheel again steered straight, the bicycle spinning inﬁnitely fast in small circles while lying ﬂat in the ground plane. (3) Lastly, a family joining a similar ﬂat spinning motion (with handlebar forward), to a handlebar-reversed limit, circling in dynamic balance at inﬁnite speed, with the frame near upright and the front wheel almost perpendicular; the transition between handlebar forward and reversed is through moderate-speed circular pivoting with the rear wheel not rotating, and the bicycle virtually upright. In the fourth part of this thesis, some of the parameters (both geometrical and inertial) for the benchmark bicycle have been changed and the resulting diﬀerent bicycles and their circular motions studied showing other families of circular motions. Finally, some of the circular motions have been examined, numerically and analytically, for stability.

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Books on the topic "Newton-Euler equations"

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Wehner, Edward. A Newton-Krylov solver for the euler equations on unstructured grids. Toronto: Deartment of Aerospace Science and Engineering, University of Toronto, 2001.

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Nichols, Jason C. A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations. [Downsview, Ont: University of Toronto, Institute for Aerospace Studies], 2004.

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1934-, Jameson Antony, and United States. National Aeronautics and Space Administration, eds. An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. [Washington, D.C.]: National Aeronautics and Space Administration, 1986.

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1934-, Jameson Antony, and United States. National Aeronautics and Space Administration, eds. An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. [Washington, D.C.]: National Aeronautics and Space Administration, 1986.

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1934-, Jameson Antony, and United States. National Aeronautics and Space Administration., eds. An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. [Washington, D.C.]: National Aeronautics and Space Administration, 1986.

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An multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations. [Washington, D.C.]: National Aeronautics and Space Administration, 1986.

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Nichols, Jason C. A three-dimensional multi-block Newton-Krylov flow solver for the Euler equations. 2004.

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Book chapters on the topic "Newton-Euler equations"

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Drela, M., M. Giles, and W. T. Thompkins. "Newton Solution of Coupled Euler and Boundary-Layer Equations." In Numerical and Physical Aspects of Aerodynamic Flows III, 143–54. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4926-9_8.

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"Newton–Euler Equations of Motion." In Engineering Dynamics, 296–390. Cambridge University Press, 2007. http://dx.doi.org/10.1017/cbo9780511805899.007.

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"◾ Euler–Newton Equations or Navier–Stokes Equations." In The Art of Fluid Animation, 58–103. A K Peters/CRC Press, 2015. http://dx.doi.org/10.1201/b19718-8.

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"Direct Dynamics: Newton–Euler Equations of Motion." In Mechanisms and Robots Analysis with MATLAB®, 183–207. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84800-391-0_5.

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A. Rendón, Manuel. "Quadrotor Unmanned Aerial Vehicles: Visual Interface for Simulation and Control Development." In Robotics Software Design and Engineering. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.97435.

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Quadrotor control is an exciting research area. Despite last years developments, some aspects demand a deeper analysis: How a quadrotor operates in challenging trajectories, how to define trajectory limits, or how changing physical characteristics of the device affects the performance. A visual interface development platform is a valuable tool to support this effort, and one of these tools is briefly described in this Chapter. The quadrotor model uses Newton-Euler equations with Euler angles, and considers the effect of air drag and propellers’ speed dynamics, as well as measurement noise and limits for propeller speeds. The tool is able to test any device just by setting a few parameters. A three-dimensional optimal trajectory defined by a set of waypoints and corresponding times, is calculated with the help of a Minimum Snap Trajectory planning algorithm. Small Angle Control, Desired Thrust Vector (DTV) Control and Geometric Tracking Control are the available strategies in the tool for quadrotor attitude and trajectory following control. The control gains are calculated using Particle Swarm Optimization. Root Mean Square (RMS) error and Basin of Attraction are employed for validation. The tool allows to choose the control strategy by visual evaluation on a graphical user interface (GUI), or analyzing the numerical results. The tool is modular and open to other control strategies, and is available in GitHub.

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Hanlon, Robert T. "Bernoulli and Euler unite Newton and Leibniz." In Block by Block: The Historical and Theoretical Foundations of Thermodynamics, 180–90. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851547.003.0011.

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Daniel Bernoulli’s Hydrodynamica was the first recorded derivation of the kinetic theory of gases and of the equation for fluid flow. He collaborated with Leonhard Euler to unite Newton’s laws of motion based on the concept of force with Leibniz’s early work on the concept of energy, which he called vis.

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Conference papers on the topic "Newton-Euler equations"

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Bongardt, B., and F. Kirchner. "Newton-Euler equations in general coordinates." In IMA Conference on Mathematics of Robotics. Institute of Mathematics and its Applications, 2015. http://dx.doi.org/10.19124/ima.2015.001.20.

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GILES, M., M. DRELA, and W. THOMPKINS, JR. "Newton solution of direct and inverse transonic Euler equations." In 7th Computational Physics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1985. http://dx.doi.org/10.2514/6.1985-1530.

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Stoneking, Eric. "Newton-Euler Dynamic Equations of Motion for a Multi-Body Spacecraft." In AIAA Guidance, Navigation and Control Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-6441.

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Manzano, Luis, Jason Lassaline, and David Zingg. "A Newton-Krylov Algorithm for the Euler Equations Using Unstructured Grids." In 41st Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-274.

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Dias, Sydney, and David Zingg. "A High-Order Parallel Newton-Krylov Flow Solver for the Euler Equations." In 19th AIAA Computational Fluid Dynamics. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-3657.

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Degrez, G., E. Issman, G. Degrez, and E. Issman. "Multilevel Newton iterative solution of Euler/Navier-Stokes equations on unstructured grids." In 13th Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-2132.

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Nichols, Jason, and David Zingg. "A Three-Dimensional Multi-Block Newton-Krylov Flow Solver for the Euler Equations." In 17th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-5230.

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Hicken, Jason, and David Zingg. "A parallel Newton-Krylov flow solver for the Euler equations on multi-block grids." In 18th AIAA Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-4333.

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Cheng, Harry Hui, and Krishna C. Gupta. "An Efficient Manipulator Dynamics Formulation Based Upon Newton-Euler Equations and the ZRP Method." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0365.

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Abstract This paper presents a formulation of robot manipulator inverse dynamics based upon the Newton-Euler equations and the zero reference position method. The angular velocities and accelerations, linear accelerations of the mass centers, and inertia forces and moments of each link of the manipulator are computed recursively starting from the base to the end-effector. But, the joint reaction forces and moments, and joint actuator forces or torques are computed recursively from the end-effector to the base. The formulation is at first carried out in the current position and then reformulated by directly utilizing the zero reference position data. The former formulation is intuitively simple; while the latter is computationally more efficient. A parametric study is also conducted to compare the relative efficiency of this formulation with the previously available formulation.

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Barman, Shuvrodeb, and Yujiang Xiang. "Recursive Newton-Euler Dynamics and Sensitivity Analysis for Robot Manipulator With Revolute Joints." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22646.

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Abstract In this study, recursive Newton-Euler sensitivity equations are derived for robot manipulator motion planning problems. The dynamics and sensitivity equations depend on the 3 × 3 rotation matrices based on the moving coordinates. Compared to recursive Lagrangian formulation, which depends on 4 × 4 Denavit-Hartenberg (DH) transformation matrices, the moving coordinate formulation increases computational efficiency significantly as the number of matrix multiplications required for each optimization iteration is greatly reduced. A two-link manipulator time-optimal trajectory planning problem is solved using the proposed recursive Newton-Euler dynamics formulation. Only revolute joint is considered in the formulation. The predicted joint torque and trajectory are verified with the data in the literature. In addition, the optimal joint forces are retrieved from the optimization using recursive Newton-Euler dynamics.

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