Relevant bibliographies by topics / Holonomic system

Academic literature on the topic 'Holonomic system'

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Published: 6 July 2023

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Journal articles on the topic "Holonomic system"

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LEVI, MARK. "GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS." International Journal of Bifurcation and Chaos 15, no. 09 (September 2005): 2747–56. http://dx.doi.org/10.1142/s0218127405013745.

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This paper gives a short overview of various applications of stabilization by vibration, along with the exposition of the geometrical mechanism of this phenomenon. More specifically, the following observation is described: a rapidly vibrated holonomic system can be approximated by a certain associated nonholonomic system. It turns out that effective forces in some rapidly vibrated (holonomic) systems are the constraint forces of an associated auxiliary nonholonomic constraint. In particular, we review a simple but remarkable connection between the curvature of the pursuit curve (the tractrix) on the one hand and the effective force on the pendulum with vibrating support. The latter observation is a part of a recently discovered close relationship between two standard classical problems in mechanics: (1) the pendulum whose suspension point executes fast periodic motion along a given curve, and (2) the Chaplygin skate (known also as the Prytz planimeter, or the "bicycle"). The former is holonomic, the latter is nonholonomic. The holonomy of the skate shows up in the effective motion of the pendulum. This relationship between the pendulum with a twirled pivot and the Chaplygin skate has somewhat unexpected physical manifestations, such as the drift of suspended particles in acoustic waves. Finally, a higher-dimensional example of "geodesic motion" on a vibrating surface is described.
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Agrawal, S. K. "Multibody Dynamics: A Formulation Using Kane’s Method and Dual Vectors." Journal of Mechanical Design 115, no. 4 (December 1, 1993): 833–38. http://dx.doi.org/10.1115/1.2919276.

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This paper proposes a formulation based on Kane’s method to form the dynamic equations of motion of multibody systems using dual vectors. Both holonomic and nonholonomic systems are considered in this formulation. An example of a holonomic and a nonholonomic system is worked out in detail using this formulation. This algorithm is shown to be advantageous for a class of holonomic systems which has cylindrical joints.
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Zhang, Sheng, and Wenjing Huang. "Application of a Propeller-Based Air Propulsion System to the Land-Based Holonomic Vehicle." Applied Sciences 9, no. 21 (November 1, 2019): 4657. http://dx.doi.org/10.3390/app9214657.

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Holonomic vehicles with wheels such as ball wheels can move in any direction without rotating. For such a system, more driving motors and precise transmission mechanisms are necessary, which makes the control and fabrication complicated. This paper aims to present the design and construction of a novel holonomic mechanism to simplify the system. Air-based propulsion was applied to a land-based holonomic vehicle. A prototype with three roller balls was developed with a propeller for the propulsion of a triangular holonomic vehicle. Only two motors were applied, one for propeller rotation and the other for the adjustment of the angle of thrust. For the establishment of the methodology, the data, including propeller size, rotation per minute, velocity, thrust, efficiency, etc., were measured or calculated. The prototype can move at a velocity of approximate 0.558 m/s with an efficiency of 18.55%. Simulation results showed that with the increase of propulsion efficiency, the velocity can achieve more than 5 m/s if the efficiency is 70%. This study is the first attempt to apply air-based propulsion to a land-based holonomic vehicle. Further, the construction method is simple and can satisfy the accuracy requirement. This design method, therefore, will contribute to the application of holonomic vehicles due to the realization of holonomic functionality and simplicity.
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Lifu, Liang, and Wei Yang. "On the unification of the Hamilton principles in non-holonomic system and in holonomic system." Applied Mathematics and Mechanics 17, no. 5 (May 1996): 457–63. http://dx.doi.org/10.1007/bf00131094.

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Ravendran, Ahalya, and Chung-Hao Hsu. "LOW COST COLLISION AVOIDANCE SYSTEM ON HOLONOMIC AND NON- HOLONOMIC MOBILE ROBOTS." MATTER: International Journal of Science and Technology 5, no. 1 (March 22, 2019): 12–22. http://dx.doi.org/10.20319/mijst.2019.51.1222.

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Neto, Orlando. "Blow up for a holonomic system." Publications of the Research Institute for Mathematical Sciences 29, no. 2 (1993): 167–233. http://dx.doi.org/10.2977/prims/1195167271.

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Cai, J. L., and F. X. Mei. "Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation." Journal of Mechanics 28, no. 3 (August 9, 2012): 589–96. http://dx.doi.org/10.1017/jmech.2012.67.

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AbstractIn this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.
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Benenti, Sergio. "The non-holonomic double pendulum: An example of non-linear non-holonomic system." Regular and Chaotic Dynamics 16, no. 5 (October 2011): 417–42. http://dx.doi.org/10.1134/s1560354711050029.

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Ariska, Melly, Hamdi Akhsan, Muhammad Muslim, Jesi Pebralia, Arini Rosa Sinensis, and Tine Aprianti. "Modeling of Dynamics Object with Non-Holonomic Constraints Based on Maple in Cylinder Coordinate R×S^1×SO(3)." JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS 14, no. 1 (December 15, 2021): 28–36. http://dx.doi.org/10.25077/jif.14.1.28-36.2022.

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Reliable real-time planning for dynamic systems is crucial in today's rapidly growing automated ecosystem, such as the environment and methods of planning a robotic system. This paper describes the rigid dynamics system with non-holonomic constraints on the R×S^1×SO(3) configuration space. The method used is the motion planning network and numeric treatment using physics computation which can be used for non-holonomic object systems that move in real-time with Jellets Invarian (JI) approach. The JI approach can result in a motion system equation and evaluate the model of an object with non-holonomic constraints and also display experimental results for navigation in the R×S^1×SO(3) configuration space. The motion system with non-holonomic constraints used is Tippe top (TT). TT is a toy like a top which when rotated will flip itself with its stem. The author have finished in simulating the dynamics of TT motions in real time with the initial states that have been described with various coordinate in the  configuration space. Based on the results of previous studies on similar objects, TT was solved by the Eular-Lagrange Equation, Routhian Reduction Equation and Poincare. The author succeeded in describing the dynamics of TT motion in real time with predetermined initial conditions with various coordinates in the R^2×SO(3) configuration space.
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Li, Liang, Renhao Zhao, and Chunlei Li. "Path Planning for Chainable Non-holonomic System Based on Iterative Learning Control." Journal Européen des Systèmes Automatisés 53, no. 5 (November 15, 2020): 747–53. http://dx.doi.org/10.18280/jesa.530518.

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Non-holonomic path planning is to solve the two point boundary value problem under constraints. Since it is offline and open-loop, the path planning cannot compensate for the disturbances and eliminate the errors. To solve the problems, this paper puts forward an iterative learning control algorithm that adjusts the control parameters of the path planner online through the multiple iterative computations of the target configuration error equation, under the initial configuration error and model error, and thus enhancing the accuracy of non-holonomic system path planning. Then, a simulation experiment on path planning was carried out for a chainable three-joint, non-holonomic manipulator. The results show that the iterative learning controller can eliminate the interference of initial configuration error and model error, such that each joint can move to the target configuration.
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Dissertations / Theses on the topic "Holonomic system"

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Yuan, Hongliang. "Control of NonH=holonomic Systems." Doctoral diss., University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2751.

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Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles' kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs.
Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Electrical Engineering PhD
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Rebahi, Yacine. "Irrégularité des D-modules algébriques holonomes." Université Joseph Fourier (Grenoble ; 1971-2015), 1996. http://www.theses.fr/1996GRE10205.

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Ce travail est consacre a l'etude de l'irregularite des systemes differentiels algebriques holonomes. Nous demontrons que les complexes de solutions de type exponentiel, associes a ces systemes, sont a cohomologie constructible et nous calculons leur caracteristique d'euler poincare. Pour cela, et dans le cas d'un fibre de rang un, nous utilisons un passage a l'infini qui nous permet de nous ramener a des resultats connus pour des solutions formelles de croissance appropriee pour des systemes analytiques holonomes. D'autre part, si nous microlocalisons nos constructions, nous obtenons des resultats analogues dans le cas d'un fibre de rang quelconque
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Delmas, Pierre. "Génération active des déplacements d'un véhicule agricole dans son environnement." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2011. http://tel.archives-ouvertes.fr/tel-00669534.

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Dans ces travaux, nous proposons un système de guidage automatique pour la navigation sûre d'un robot mobile dans un monde ouvert. Le principe est de contrôler la direction et la vitesse du véhicule afin de préserver son intégrité physique et celle de son environnement. Cela se traduit par la généralisation du concept d'obstacle permettant d'estimer l'espace de vitesses admissibles par le véhicule en fonction de la surface de navigation, des capacités du véhicule et de son état. Afin d'atteindre cet objectif, le système doit pour chaque itération : 1) fournir à la tâche de perception une zone sur laquelle elle devra focaliser son attention pour la reconstruction de l'environnement ; 2) générer des trajectoires admissibles par le véhicule ; 3) estimer le profil de vitesse admissible pour chacune d'entre elles ; 4) pour finir, sélectionner la plus optimale par rapport à un critère prédéfini. Des résultats simulés et obtenus sur un démonstrateur réel permettent d'analyser les performances obtenues du système face à des scénarios divers et en démontre la pertinence.
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Ortiz, Morales Daniel. "Virtual Holonomic Constraints: from academic to industrial applications." Doctoral thesis, Umeå universitet, Institutionen för tillämpad fysik och elektronik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-87707.

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Whether it is a car, a mobile phone, or a computer, we are noticing how automation and production with robots plays an important role in the industry of our modern world. We find it in factories, manufacturing products, automotive cruise control, construction equipment, autopilot on airplanes, and countless other industrial applications.         Automation technology can vary greatly depending on the field of application. On one end, we have systems that are operated by the user and rely fully on human ability. Examples of these are heavy-mobile equipment, remote controlled systems, helicopters, and many more. On the other end, we have autonomous systems that are able to make algorithmic decisions independently of the user.         Society has always envisioned robots with the full capabilities of humans. However, we should envision applications that will help us increase productivity and improve our quality of life through human-robot collaboration. The questions we should be asking are: “What tasks should be automated?'', and “How can we combine the best of both humans and automation?”. This thinking leads to the idea of developing systems with some level of autonomy, where the intelligence is shared between the user and the system. Reasonably, the computerized intelligence and decision making would be designed according to mathematical algorithms and control rules.         This thesis considers these topics and shows the importance of fundamental mathematics and control design to develop automated systems that can execute desired tasks. All of this work is based on some of the most modern concepts in the subjects of robotics and control, which are synthesized by a method known as the Virtual Holonomic Constraints Approach. This method has been useful to tackle some of the most complex problems of nonlinear control, and has enabled the possibility to approach challenging academic and industrial problems. This thesis shows concepts of system modeling, control design, motion analysis, motion planning, and many other interesting subjects, which can be treated effectively through analytical methods. The use of mathematical approaches allows performing computer simulations that also lead to direct practical implementations.
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Töyrä, Daniel. "Fidelity of geometric and holonomic quantum gates for spin systems." Thesis, Uppsala universitet, Teoretisk kemi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-222152.

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Geometric and holonomic quantum gates perform transformations that only dependon the geometry of a loop covered by the parameters controlling the gate. Thesegates require adiabatic time evolution, which is achieved in the limit when the looptakes infinite time to complete. However, it is of interest to also know thetransformation properties of the gates for finite run times. It has been shown [Phys.Rev. A 73, 022327 (2006)] that some holonomic gates for a trapped ion system showrevival structures, i.e., for some finite run time the gate performs the sametransformation as it does in the adiabatic limit. The purpose of this thesis is to investigate if similar revival structures are shown alsofor geometric and holonomic quantum gates for spin systems. To study geometricquantum gates an NMR setup for spin-1/2 particles is used, while an NQR setup forspin-3/2 particles is used to study holonomic quantum gates. Furthermore, for thegeometric quantum gates the impact of some open system effects are examined byusing the quantum jump approach. The non-adiabatic time evolution operators of thesystems are calculated and compared to the corresponding adiabatic time evolutionoperators by computing their operator fidelity. The operator fidelity ranges between0 and 1, where 1 means that the gates are identical up to an unimportant phasefactor. All gates show an oscillating dependency on the run time, and some Abeliangates even show true revivals, i.e., the operator fidelity reaches 1.
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Stroot, Holger [Verfasser]. "Strong Approximation of Stochastic Mechanical Systems with Holonomic Constraints / Holger Stroot." München : Verlag Dr. Hut, 2019. http://d-nb.info/1196415595/34.

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Frolík, Stanislav. "Geometrická teorie řízení na nilpotentních Lieových grupách." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-399583.

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This thesis deals with the theory of geometric control of the trident robot. The thesis describes the basic concepts of differential geometry and control theory, which are subsequently used for describing various mechanisms. Finally, the thesis proposes the management using inferred results.
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Seiler, Konstantin. "Fast trajectory generation and correction for non-holonomic systems exploiting Lie group symmetries." Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/10117.

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Sampling based motion planning is a popular motion planning technique for systems with many degrees of freedom in continuous state spaces. In particular the class of Rapidly exploring Random Tree algorithms (RRTs) has wide-spread use as they can be applied to a broad range of systems. Subsequently many extensions and variations to the RRT algorithm are known today. Many results, however, are not applicable in the case of non-holonomic and underactuated systems due to the difficulty in obtaining the required length-of-shortest-path distance metric and corresponding local planner. Instead, by focussing on changing existing paths this work develops algorithmic frameworks that allow faster motion planning specifically in the domain of non-holonomic underactuated systems. In order to adapt the paths efficiently, symmetries exhibited by the system are exploited by the algorithms. The particular focus of this work is on continuous symmetry groups that constitute a Lie group and thus allow for fast and powerful transformations of existing trajectories. Two methods are proposed to address this. The first allows path correction of an arbitrary path to reach a given goal. It works by applying small changes to selected small segments of a given trajectory and propagates their effects in a fast way using symmetry operations that avoid costly reintegration along the whole path. The second method allows the RRT algorithm to plan for a whole family of paths simultaneously to achieve greater coverage of the state space. The algorithm identifies those symmetry orbits, or subspaces thereof, that contain valid paths and propagates their states throughout the planning process. Both methods can be employed together and complement each other well.
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Mauny, Johan Raphaël. "Modélisation dynamique des systèmes non-holonomes intermittents : application à la bicyclette." Thesis, Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2018. http://www.theses.fr/2018IMTA0113.

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Cette thèse traite de la modélisation dynamique des systèmes non-holonomes intermittents et de son application à la bicyclette 3D de Whipple. Pour cela, nous nous sommes appuyés sur un ensemble d'outils en mécanique géométrique (réduction Lagrangienne et projection dans le noyau des contraintes cinématiques essentiellement). Dans un premier temps, nous avons traité le cas de la bicyclette persistante. En définissant l'espace des configurations du vélo comme un fibré principal de groupe structural SE(3), nous avons obtenu un modèle des points de contact et des contraintes exempt de toute non-linéarité associée à un paramétrage de type coordonnées généralisées. Cette formulation nous a permis d'obtenir le noyau des contraintes sous une forme symbolique sans singularité. Nous avons alors produit un modèle symbolique de la dynamique de la bicyclette persistante en utilisant la méthode de réduction par projection de sa dynamique libre dans le sous espace de ses vitesses admissibles. Cette approche étend le cadre général mis au point ces dernières années pour la locomotion bio-inspirée. Profitant de la structure de SE(3), un modèle de la bicyclette intermittente a été proposé dans le cadre d'une approche événementielle. L'adoption du modèle physique de l'impact plastique, nous a permis d'étendre la méthode de réduction par projection au cas intermittent. Nous avons alors comparé notre approche "réduite" à l'approche classiquement utilisée et avons montré qu'elles partageaient une interprétation géométrique commune. Ces outils ont finalement été appliqués à la simulation de la bicyclette intermittente afin d'illustrer la richesse de sa dynamique
This thesis deals with the dynamic modelling of intermittent non-holonomic systems andits application to the Whipple 3D bicycle. To that end, we relied on a set of tools in geometric mechanics (mainly Lagrangian reduction and the projection in the kernel of the kinematic constraints). In the first instance, we have addressed the case of the bicycle subjected to persistent contacts. By defining the space of the bicycle configurations as a principal fibre bundle with SE(3) as structural group, we obtained a model of the contact points and of the constraints free of any non-linearities associated with a generalized coordinate type configuration. This formulation allowed us to obtain the kernel of the constraints in a symbolic form without singularity. We then produced a symbolic model of the dynamics ofthe bicycle subjected to persistent contacts using the projection reduction method of its free dynamics in the subspace of its permissible speeds. This approach extends the general framework developed in recent years for bio-inspired locomotion. Taking advantage of the structure of SE(3), a model of the intermittent bicycle was proposed as part of an event-driven approach. Moreover, the adoption ofthe physical model of plastic impact has allowed us to extend the projection reduction method to the intermittent case. We then compared our "reduced" approach to the conventional approach and showed that they shared a common geometric interpretation. These tools were finally applied to the simulation of the intermittent bicycle to illustrate its rich dynamics
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Abdel, Gadir Basil. "Analyse microlocale des systèmes différentiels holonomes." Grenoble 1, 1992. http://www.theses.fr/1992GRE10071.

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Nous nous placerons dans le contexte analytique-complexe. Les systemes differentiels holonomes traduisent algebriquement les systemes differentiels lineaires surdetermines maximaux, et ils generalisent les fibres vectoriels a connexion integrale. La question de leur classification (jusqu'ici limitee au cas des systemes a singularite reguliere et a celui d'une variable) a ete entreprise par un certain nombre d'auteurs, parmi lesquels il faut notamment citer m. Kashiwara et b. Malgrange. Dans cette direction nous contribuons aux resultats lies a la description microlocale (i. E. Locale sur l'espace cotangent) des systemes differentiels holonomes a singularite arbitraire. Nous generalisons un theoreme de finitude de b. Malgrange en utilisant un lemme de m. Kashiwara et t. Kawai affirmant que le germe du support d'un systeme microdifferentiel holonome possede (apres une transformation symplectique convenable) une position generique. Le theoreme de finitude assure qu'un tel systeme microdifferentiel admet un reseau microdifferentiel de type fini sur l'anneau commutatif des fonctions holomorphes. A l'aide de ce resultat, nous demontrons que ces systemes microdifferentiels holonomes sont en fait des systemes differentiels holonomes. En outre, nous formulons et nous etudions la transformation de fourier-deligne-katz-laumon-malgrange pour les systemes differentiels holonomes ainsi trouves. Ici, le resultat interessant est que l'etude de tels objets se ramene a celle des connexions meromorphes etudiee par p. Deligne et b. Malgrange
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Books on the topic "Holonomic system"

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Soltakhanov, Shervani Kh, Mikhail P. Yushkov, and Sergei A. Zegzhda. Mechanics of non-holonomic systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85847-8.

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Conference on Geometric Control and Non-holonomic Mechanics (1996 Mexico City, Mexico). Geometric control and non-holonomic mechanics: Conference on Geometric Control and Non-holonomic Mechanics, June 19-21, 1996, Mexico City. Edited by Jurdjevic Velimir and Sharpe R. W. Providence, R.I: American Mathematical Society, 1998.

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Saito, Mutsumi. Gröbner deformations of hypergeometric differential equations. Berlin: Springer, 2000.

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Geometric, control, and numerical aspects of nonholonomic systems. Berlin: Springer, 2002.

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Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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Soltakhanov, Sh Kh, Mikhail Yushkov, and S. Zegzhda. Mechanics of Non-Holonomic Systems: A New Class of Control Systems. Springer London, Limited, 2009.

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Soltakhanov, Sh Kh, Mikhail Yushkov, and S. Zegzhda. Mechanics of Non-Holonomic Systems: A New Class of Control Systems. Springer Berlin / Heidelberg, 2010.

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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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Saito, Mutsumi, Nobuki Takayama, and Bernd Sturmfels. Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6. Springer, 2000.

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Book chapters on the topic "Holonomic system"

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Liu, Hongfang, Ruijuan Li, and Nana Li. "Hamilton Non-holonomic Momentum Equation of the System and Conclusions." In Communications in Computer and Information Science, 23–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-27503-6_4.

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Wang, ZhiDong, Yoshio Kimura, Takayuki Takahashi, and Eiji Nakano. "A Control Method of a Multiple Non-holonomic Robot System for Cooperative Object Transportation." In Distributed Autonomous Robotic Systems 4, 447–56. Tokyo: Springer Japan, 2000. http://dx.doi.org/10.1007/978-4-431-67919-6_42.

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Andreev, Aleksandr, and Olga Peregudova. "On the Control Models in the Trajectory Tracking Problem of a Holonomic Mechanical System." In Lecture Notes in Electrical Engineering, 686–95. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58653-9_66.

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Cuenca Macas, Leduin José, and Israel Pineda. "Collision Avoidance Simulation Using Voronoi Diagrams in a Centralized System of Holonomic Multi-agents." In Information and Communication Technologies, 18–31. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18272-3_2.

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Haraoka, Yoshishige. "Holonomic Systems." In Trends in Mathematics, 59–87. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52842-7_2.

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Soltakhanov, Shervani Kh, Mikhail P. Yushkov, and Sergei A. Zegzhda. "Holonomic Systems." In Foundations of Engineering Mechanics, 1–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85847-8_1.

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Umerez, Jon, and Matteo Mossio. "Constraint, Holonomic." In Encyclopedia of Systems Biology, 494. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_706.

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Umerez, Jon, and Matteo Mossio. "Constraint, Non-holonomic." In Encyclopedia of Systems Biology, 494. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_707.

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Saito, Mutsumi, Bernd Sturmfels, and Nobuki Takayama. "Solving Regular Holonomic Systems." In Gröbner Deformations of Hypergeometric Differential Equations, 51–102. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04112-3_2.

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Björk, Jan-Erik. "Distributions and regular holonomic systems." In Analytic D-Modules and Applications, 281–332. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0717-6_8.

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Conference papers on the topic "Holonomic system"

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Varszegi, Balazs, Denes Takacs, and Gabor Stepan. "Skateboard: A Human Controlled Non-Holonomic System." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47512.

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A simple mechanical model of the skateboard-skater system is analyzed, in which a linear PD controller with delay is included to mimic the effect of human control. The equations of motion of the non-holonomic system are derived with the help of the Gibbs-Appell method. The linear stability analysis of rectilinear motion is carried out analytically using the D-subdivision method. It is shown how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as a function of the speed and the fore-aft location of the skater on the board. Based on these, an explanation is given for the well-known instability of the skateboard-skater system at high speed.
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Terze, Zdravko, Dubravko Matijasˇevic´, Milan Vrdoljak, and Vladimir Koroman. "Differential-Geometric Characteristics of Optimized Generalized Coordinates Partitioned Vectors for Holonomic and Non-Holonomic Multibody Systems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86849.

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Differential-geometric characteristics and structure of optimized generalized coordinates partitioned vectors for generally constrained multibody systems are discussed. Generalized coordinates partitioning is well-known procedure that can be applied in the framework of numerical integration of DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for coordinates partitioning is needed to obtain the best performance. After short presentation of differential-geometric background of optimized coordinates partitioning, the structure of optimally partitioned vectors is discussed on the basis of gradient analysis of separate constraint submanifolds at configuration and velocity level when holonomic and non-holonomic constraints are present in the system. While, in the case of holonomic systems, the vectors of optimally partitioned coordinates have the same structure for generalized positions and velocities, when non-holonomic constraints are present in the system, the optimally partitioned coordinates generally differ at configuration and velocity level and separate partitioned procedure has to be applied. The conclusions of the paper are illustrated within the framework of the presented numerical example.
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Koganezawa, Koichi, and Kazuomi Kaneko. "ODE Methods for Solving the Multibody Dynamics With Constraints." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8237.

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Abstract This paper deals with methods for solving the multi-body dynamics with constraints. The problem is considered in the framework of solving the Lagrange multipliers in addition to the system coordinates in the differential and algebraic equation (DAE) governing the dynamics with holonomic or non-holonoinic constraints. The proposed methods are originally based on Baumgarte’s work for the holonomic constraints but its extensions. First, one considers a Lagrangian which includes the time-differentiated constraint equations in addition to the constraint equations themselves. Applying the Lagrange procedure we have the ordinary differential equations (ODE), not the DAE, including the differential equation with respect to the Lagrange multipliers. This paper also presents a numerically stable method for inverting the system matrix. The numerical solution for the differential equations with respect to the Lagrange multipliers as well as the system coordinates by using the ordinary numerical integration method, e.g. Runge-Kutta method, shows the excellent stability of the constraints, which is superior to the penalty method.
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Iori, Tomoyuki. "On First Integrals of Hamiltonian System with Holonomic Hamiltonian." In 2022 IEEE 61st Conference on Decision and Control (CDC). IEEE, 2022. http://dx.doi.org/10.1109/cdc51059.2022.9992319.

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Koganezawa, Koichi, and Kazuomi Kaneko. "A Method for Constraints Stabilization on Solving Multibody Dynamics." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21322.

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Abstract This paper deals with methods for solving the multibody dynamics with constraints. The problem is considered in the framework of solving the Lagrange multipliers in addition to the system coordinates in the differential and algebraic equation (DAE) governing the dynamics with holonomic or non-holonomic constraints. The proposed methods are originally based on Baumgarte’s work for the holonomic constraints but its extensions to the non-holonomic constraints. Conventionally the Lagrange multipliers are solved algebraically and substituted into the dynamic equations (DAE). This paper, on the other hand, proposes a method to derive the ordinary differential equations with respect to the Lagrange multipliers. One can resort the ordinary numerical integration method to solve the Lagrange multipliers as same as to solve the ODE with respect to the system coordinates. Some examples of numerical solution for the mechanical models having holonomic and non-holonomic constraints shows the excellent stability of the constraints, which is superior to the Baumgarte’s stabilizing method and the penalty method.
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Seguy, N., P. Joli, Z. Q. Feng, and M. Pascal. "A Modular Dynamic Model for Multibody System Adapted to Interactive Simulation." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48311.

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This paper presents a modular model of rigid multibody system using the acceleration-based augmented Lagrangian formulation. An important effort on the formulation of the governing equations has been made in order to meet the requirements for interactive simulation in computer aided design. Each body has been considered as an independent numerical component with its own numerical parameters, own mechanical parameters and own numerical integration scheme. Non-holonomic and holonomic constraints have been implemented in this formulation. This present work can be considered as an extended formulation of Bayo et al. [1] to the problem of interactive design and particular attention is paid to define the criteria of numerical stability.
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Tang, Chin Pei. "Configuration optimization for multiple nonholonomic mobile manipulators with holonomic interaction." In 2010 42nd Southeastern Symposium on System Theory (SSST 2010). IEEE, 2010. http://dx.doi.org/10.1109/ssst.2010.5442833.

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Yoshimura, Hiroaki. "A Geometric Approach to Constraint Stabilization for Holonomic Lagrangian Systems." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35429.

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In this paper, we develop a geometric approach to constraint stabilization for holonomic mechanical systems in the context of Lagrangian formulation. We first show that holonomic mechanical systems, for the case in which a given Lagrangian is hyperregular, can be formulated by using the Lagrangian two-form, namely, a symplectic structure on the tangent bundle of a configuration manifold that is induced from the cotangent bundle via the Legendre transformation. Then, we present an idea of geometric constraint stabilization and we show that a holonomic Lagrangian system with geometric constraint stabilization can be formulated by the Lagrange-d’Alembert principle, together with its local coordinate expression for the sake of numerical computations. Finally, we illustrate the numerical verification that the proposed method enables to stabilize constraint violations effectively in comparison with the Baumgarte and Gear–Gupta–Leimkuhler methods together with an example of a linkage mechanism.
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Terze, Zdravko, and Joris Naudet. "Discrete Mechanical Systems: Projective Constraint Violation Stabilization Method for Numerical Forward Dynamics on Manifolds." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35466.

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During numerical forward dynamics of discrete mechanical systems with constraints, a numerical violation of system kinematical constraints is the basic source of time-integration errors and frequent difficulty that analyst has to cope with. The stabilized time-integration procedure, whose stabilization step is based on projection of the integration results to the underlying constraint manifold via post-integration correction of the selected coordinates, is proposed in the paper. After discussing optimization of the partitioning algorithm, the geometric and stabilization issues of the method are addressed and it is shown that the projective stabilization algorithm can be applied for numerical stabilization of holonomic and non-holonomic constraints in Pfaffian and general form. As a continuation of the previous work, a further elaboration of the projective stabilization method applied on non-holonomic discrete mechanical systems is reported in the paper and numerical example is provided.
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Yoshimura, Hiroaki, and Kenji Soya. "On the Geometric Stabilization for Discrete Hamiltonian Systems With Holonomic Constraints." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86354.

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This paper develops a discrete Hamiltonian system with holonomic constraints with Geometric Constraint Stabilization. It is first shown that constrained mechanical systems with nonconservative external forces can be formulated by using canonical symplectic structures in the context of Hamiltonian systems. Second, it is shown that discrete holonomic Hamiltonian systems can be developed via the discretization based on the Backward Differentiation Formula and also that geometric constraint stabilization can be incorporated into the discrete Hamiltonian systems. It is demonstrated that the proposed method enables one to stabilize constraint violations effectively in comparison with conventional methods such as Baumgarte Stabilization and Gear–Gupta–Leimkuhler Stabilization, together with an illustrative example of linkage mechanisms.
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