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Journal articles on the topic 'Holonomic system'

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Published: 6 July 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Zhang, Yao Yu, Xian Ting Sun, Xi Chang Xue, and Li Qun Jia. "Conformal Invariance and Conserved Quantity of Mei Symmetry for Appell Equations in a Holonomic System with Mass Variable." Applied Mechanics and Materials 670-671 (October 2014): 617–25. http://dx.doi.org/10.4028/www.scientific.net/amm.670-671.617.

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For a holonomic system with variable mass, the conformal invariance and the conserved quantity of Mei symmetry of Appell equations are investigated. First, by the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the Mei symmetry and the conformal invariance of differential equations of motion for Appell equations in a holonomic system with variable mass are defined, and the determining equation of Mei symmetry and conformal invariance for Appell equations in a holonomic system with variable mass are given. Then, the Mei-conserved quantity corresponding to the system is derived by means of the structure equation to which the gauge function satisfies. Finally, an example is given to illustrate the application of the result.
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12

Bhattacharyya, Shaman, and Somnath Bhattacharyya. "Demonstration of the Holonomically Controlled Non-Abelian Geometric Phase in a Three-Qubit System of a Nitrogen Vacancy Center." Entropy 24, no. 11 (November 2, 2022): 1593. http://dx.doi.org/10.3390/e24111593.

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The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. Considering this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (~85%) of three-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate’s dark state with the qubit’s initial state hence decoherence of the multi-qubit system is well-controlled through a π/3 rotation.
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13

Sanh, Do. "A form of equations of motion of a mechanical system in quasi-coordinates." Vietnam Journal of Mechanics 21, no. 1 (March 30, 2000): 45–56. http://dx.doi.org/10.15625/0866-7136/9986.

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In [3, 4, 5] the form of equations of motion in holonomic coordinates has constructed. The equations obtained give an effective tool for investigating complicated systems. In the present paper the form of equations of motion is written in quasi-coordinates. These equations are solved with respect to quasi-accelerations, which allow to define the motion of a holonomic and nonholonomic systems by a closed set of algebraic – differential equations. The reaction forces of constraints imposed on the system under consideration are calculated by means of a simple algorithm. For illustrating the effectiveness of this form of equations an example is considered.
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14

Shen-Yang, Shi, Chen Li-Qun, and Fu Jing-Li. "Mei Symmetry of General Discrete Holonomic System." Communications in Theoretical Physics 50, no. 3 (September 2008): 607–10. http://dx.doi.org/10.1088/0253-6102/50/3/14.

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15

ZHANG, Yi. "A Study on Time Scale Non-Shifted Hamiltonian Dynamics and Noether's Theorems." Wuhan University Journal of Natural Sciences 28, no. 2 (April 2023): 106–16. http://dx.doi.org/10.1051/wujns/2023282106.

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The time-scale non-shifted Hamiltonian dynamics are investigated, including both general holonomic systems and nonholonomic systems. The time-scale non-shifted Hamilton principle is presented and extended to nonconservative system, and the dynamic equations in Hamiltonian framework are deduced. The Noether symmetry, including its definition and criteria, for time-scale non-shifted Hamiltonian dynamics is put forward, and Noether's theorems for both holonomic and nonholonomic systems are presented and proved. The non-shifted Noether conservation laws are given. The validity of the theorems is verified by two examples.
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16

Papastavridis, John G. "The Maggi or Canonical Form of Lagrange’s Equations of Motion of Holonomic Mechanical Systems." Journal of Applied Mechanics 57, no. 4 (December 1, 1990): 1004–10. http://dx.doi.org/10.1115/1.2897618.

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This paper formulates the simplest possible, or canonical, form of the Lagrangean-type of equations of motion of holonomically constrained mechanical systems. This is achieved by introducing a new special set of n holonomic (system) coordinates in terms of which the m ( < n) holonomic constraints are expressed in their simplest, or uncoupled, form: the first m of these new coordinates vanish; the remaining (n-m) (nonvanishing) new coordinates of the (n-m) degree-of-freedom system are then independent. From the resulting equations of motion: (a) The last (n-m) are reactionless canonical equations (the holonomic counterpart of the linear or nonlinear equations, either of Maggi (in the old variables), or of Boltzmann/Hamel (in the new variables)) whose solution yields the motion, while (b) the first m supply the system reactions, in the old or new coordinates, once the motion is known. Special forms of these equations and a simple example are also given. The geometrical interpretation of the above, in modern vector/linear algebra language is summarized in the Appendix.
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17

Sumbatov, Alexander S. "Invariant Characterization of Liouville’s System with Two Degrees of Freedom." International Journal of Applied Mathematics, Computational Science and Systems Engineering 4 (December 2, 2022): 74–76. http://dx.doi.org/10.37394/232026.2022.4.9.

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The local problem of finding separated generalized coordinates in a holonomic natural system with two degrees of freedom (if the solution exists) is reduced to the problem of integrability of the Pfaffian systems of differential equations.
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18

Zeidis, Igor, Klaus Zimmermann, Steffen Greiser, and Julia Marx. "Analysis of Kinematic Constraints in the Linkage Model of a Mecanum-Wheeled Robot and a Trailer with Conventional Wheels." Applied Sciences 13, no. 13 (June 23, 2023): 7449. http://dx.doi.org/10.3390/app13137449.

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Mechanical systems that consist of a four-wheeled or two-wheeled robot with Mecanum wheels and a two-wheeled trailer with conventional wheels are considered. The kinematic characteristics of the mechanical systems under consideration of holonomic and non-holonomic constraints are presented and compared. From this, it is shown that the structure of the kinematic constraint equations for mobile systems with a trailer does not apply to Chaplygin’s dynamic equations. If the mechanical system is not Chaplygin’s system, then the dynamic equations cannot be integrated separately from the equations of kinematic constraints. This is the difference between the kinematic constraint equations for the robot-trailer system and the constraint equations for a single robot with Mecanum wheels. Examples of numerical calculations using the equations of kinematic constraints are given.
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19

Han, Y. L., X. X. Wang, M. L. Zhang, and L. Q. Jia. "Lie Symmetry and Approximate Hojman Conserved Quantity of Lagrange Equations for a Weakly Nonholonomic System." Journal of Mechanics 30, no. 1 (August 8, 2013): 21–27. http://dx.doi.org/10.1017/jmech.2013.47.

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ABSTRACTThe Lie symmetry and Hojman conserved quantity of Lagrange equations for a weakly nonholonomic system and its first-degree approximate holonomic system are studied. The differential equations of motion for the system are established. Under the special infinitesimal transformations of group in which the time is invariable, the definition of the Lie symmetry for the weakly nonholonomic system and its first-degree approximate holonomic system are given, and the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are obtained. Finally, an example is given to study the exact and approximate Hojman conserved quantity for the system.
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20

Cao, Kien Van, and Anh Pham Huy Ho. "Pendubot trajectory planning and control using virtual holonomic constraint approach." Science and Technology Development Journal 18, no. 3 (August 30, 2015): 76–85. http://dx.doi.org/10.32508/stdj.v18i3.887.

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In this paper, the virtual holonomic constraint approach is initiatively applied for the trajectory planning and control design of a typical double link underactuated mechanical system, called the Pendubot. The goal is to create synchronous oscillations of both links. After modeling the system using Euler-Lagrangian equations of motion, the parameters of the model are identified with optimization techniques. Using this model, the trajectory planning is done via Virtual Holonomic Constraint approach on the basis of re-parameterization of the motion according to geometrical relations among the generalized coordinates of the system.
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21

Khusanov, K. "Stabilization of mechanical system with holonomic servo constraints." IOP Conference Series: Materials Science and Engineering 883 (July 21, 2020): 012146. http://dx.doi.org/10.1088/1757-899x/883/1/012146.

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22

Shi-Wang, Zheng, Jia Li-Qun, and Yu Hong-Sheng. "Mei symmetry of Tzénoff equations of holonomic system." Chinese Physics 15, no. 7 (July 2006): 1399–402. http://dx.doi.org/10.1088/1009-1963/15/7/001.

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23

Xing, Tonghao, and Dianmin Tong. "Nonadiabatic holonomic quantum computation with atom-cavity system." Chinese Science Bulletin 65, no. 23 (April 10, 2020): 2499–506. http://dx.doi.org/10.1360/tb-2020-0265.

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24

Fang Jian-Hui, Ding Ning, and Wang Peng. "Noether-Lie symmetry of non-holonomic mechanical system." Acta Physica Sinica 55, no. 8 (2006): 3817. http://dx.doi.org/10.7498/aps.55.3817.

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25

Pitanga, P. "Quantization of a non-holonomic system with symmetry." Il Nuovo Cimento B Series 11 109, no. 6 (June 1994): 583–94. http://dx.doi.org/10.1007/bf02728440.

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26

Härkönen, Marc, Tomonari Sei, and Yoshihiro Hirose. "Holonomic extended least angle regression." Information Geometry 3, no. 2 (October 8, 2020): 149–81. http://dx.doi.org/10.1007/s41884-020-00035-1.

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AbstractOne of the main problems studied in statistics is the fitting of models. Ideally, we would like to explain a large dataset with as few parameters as possible. There have been numerous attempts at automatizing this process. Most notably, the Least Angle Regression algorithm, or LARS, is a computationally efficient algorithm that ranks the covariates of a linear model. The algorithm is further extended to a class of distributions in the generalized linear model by using properties of the manifold of exponential families as dually flat manifolds. However this extension assumes that the normalizing constant of the joint distribution of observations is easy to compute. This is often not the case, for example the normalizing constant may contain a complicated integral. We circumvent this issue if the normalizing constant satisfies a holonomic system, a system of linear partial differential equations with a finite-dimensional space of solutions. In this paper we present a modification of the holonomic gradient method and add it to the extended LARS algorithm. We call this the holonomic extended least angle regression algorithm, or HELARS. The algorithm was implemented using the statistical software , and was tested with real and simulated datasets.
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27

Florio, Giuseppe. "Decoherence in Holonomic Quantum Computation." Open Systems & Information Dynamics 13, no. 03 (September 2006): 263–72. http://dx.doi.org/10.1007/s11080-006-9006-2.

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Geometric phases are an interesting field of research in quantum mechanics. Recently both abelian and nonabelian geometric phases have been proposed as a useful resource for the experimental implementation of quantum computation. In this paper we focus on a particular physical model and study the effect of a bosonic bath on a class of holonomic transformations. We write a general master equation for time-dependent Hamiltonians and derive analytical and numerical solutions for the system considered. The fidelity is analyzed in the adiabatic and nonadiabatic regime. We also determine an optimal finite operation time for this class of gates.
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28

Ge Wei-Kuan. "Mei symmetry and conserved quantity of a holonomic system." Acta Physica Sinica 57, no. 11 (2008): 6714. http://dx.doi.org/10.7498/aps.57.6714.

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29

Sarafian, Haiduke, and Nenette Hickey. "Characteristics of a Two-Body Holonomic Constraint Mechanical System." World Journal of Mechanics 07, no. 06 (2017): 161–66. http://dx.doi.org/10.4236/wjm.2017.76014.

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30

Sarafian, Haiduke. "Kinematics of a Holonomic Constraint Rod & Cube System." World Journal of Mechanics 08, no. 06 (2018): 227–35. http://dx.doi.org/10.4236/wjm.2018.86018.

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31

Zhang Xiang-Wu. "Higher order Lagrange equations of holonomic potential mechanical system." Acta Physica Sinica 54, no. 10 (2005): 4483. http://dx.doi.org/10.7498/aps.54.4483.

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32

Andreev, A. S., and O. A. Peregudova. "On stabilization of program motions of holonomic mechanical system." Automation and Remote Control 77, no. 3 (March 2016): 416–27. http://dx.doi.org/10.1134/s0005117916030048.

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33

ARJONILLA GARCIA, Francisco J., and Yuichi KOBAYASHI. "Acquisition of observer mapping in driftless, non-holonomic system." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2020 (2020): 2P2—I09. http://dx.doi.org/10.1299/jsmermd.2020.2p2-i09.

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34

Wu, Hui-Bin, and Feng-Xiang Mei. "Symmetry of Lagrangians of a holonomic variable mass system." Chinese Physics B 21, no. 6 (June 2012): 064501. http://dx.doi.org/10.1088/1674-1056/21/6/064501.

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35

Papalexiou, Nikolaos. "Formal extension and quotients of the invariant holonomic system." Journal of Pure and Applied Algebra 210, no. 3 (September 2007): 685–94. http://dx.doi.org/10.1016/j.jpaa.2006.11.010.

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36

SOYA, Kenji, and Hiroaki YOSHIMURA. "484 Discrete Holonomic Hamiltonian system with Geometric Constraint Stabilization." Proceedings of the Dynamics & Design Conference 2009 (2009): _484–1_—_484–5_. http://dx.doi.org/10.1299/jsmedmc.2009._484-1_.

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37

Shi, Heng, Yanbing Liang, and Zhaohui Liu. "An approach to the dynamic modeling and sliding mode control of the constrained robot." Advances in Mechanical Engineering 9, no. 2 (February 2017): 168781401769047. http://dx.doi.org/10.1177/1687814017690470.

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An approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. On the basis of the Udwadia–Kalaba approach, the explicit equation of the constrained robot system is obtained first. This equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. Second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the end-effector on a vertical constrained surface to obtain actual values of the unknown constraint force. Moreover, model order reduction method is innovatively used in the Udwadia–Kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. Based on the demonstration of this novel method, a detailed robot system example is finally presented.
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38

Fujiwara, Shigeki, Hitoshi Kitano, Hideki Yamashita, Hiroshi Maeda, and Hideo Fukunaga. "Omnidirectional Cart with Power-assist System." Journal of Robotics and Mechatronics 14, no. 4 (August 20, 2002): 333–41. http://dx.doi.org/10.20965/jrm.2002.p0333.

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We provided a holonomic omnidirectional cart using a universal wheel with the power-assist function and put it into practical use as a meal delivery cart. Even if the cart weighs about 700 kilograms, it is easily operated as a manually operated lightweight cart. This report gives an overview of the new product, measures for enhancing operability, a handle sensing force in 3 directions, measures to reduce vibration during universal wheel driving, and ways to improve universal wheel durability.
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39

Tang, Chin Pei, and Venkat N. Krovi. "Manipulability-based configuration evaluation of cooperative payload transport by mobile manipulator collectives." Robotica 25, no. 1 (August 24, 2006): 29–42. http://dx.doi.org/10.1017/s0263574706002979.

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In this paper, we focus on the development of a quantitative performance analysis framework for a cooperative system of multiple wheeled mobile manipulators physically transporting a common payload. Each mobile manipulator module consists of a differentially driven wheeled mobile robot (WMR) with a mounted planar three-degree-of-freedom (DOF) revolute-jointed manipulator. A composite cooperative system is formed when a payload is placed at the end-effectors of many such modules. The system possesses the ability to change its relative configuration as well as to accommodate relative positioning errors of the wheeled agents. However, the combination of nonholonomic constraints due to the mobile bases, holonomic constraints due to the closed kinematic loops, and the different joint-actuation schema (active/passive/locked) within the system requires careful quantitative evaluation to efficiently realize the payload manipulation task. Hence, in this paper, we extend the differential kinematic model for treatment of constrained articulated mechanical systems to formulate a framework to include both the mixture effect of holonomic/nonholonomic constraints and the different possible joint-actuation schema in our system. The system-level performance is then examined quantitatively by the manipulability measure in terms of isotropy index with representative case studies.
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40

Náprstek, Jiří, and Cyril Fischer. "Singular solutions of a non-holonomic system as limits separating solution groups of particular type." MATEC Web of Conferences 211 (2018): 04001. http://dx.doi.org/10.1051/matecconf/201821104001.

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The non-holonomic system represents a model of the ball tuned mass damper (TMD), as used to absorb vibration of selected engineering structures, where conventional absorber types are inapplicable. The device consists of a ball moving within a spherical cavity fixed with the structure. To deduce a governing differential system the Appel-Gibbs formulation has been employed. The non-linear mathematical model includes six degrees of freedom and three non-holonomic constraints. The system has an auto-parametric character. The homogeneous differential system in the normal form is formulated. Its general properties are investigated for various settings of non-homogeneous initial conditions. Several singular solutions are extracted and physically interpreted. In principal, they represent limits separating solution groups of a certain character. The shape and general character of regular solutions within individual domains staked out by these limits are analyzed in order to facilitate a practical application of this theoretical background.
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41

Cantarelli, Giancarlo. "Global existence and boundedness for quasi-variational systems." International Journal of Mathematics and Mathematical Sciences 22, no. 2 (1999): 281–311. http://dx.doi.org/10.1155/s0161171299222818.

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We consider quasi-variational ordinary differential systems, which may be considered as the motion law for holonomic mechanical systems. Even when the potential energy of the system is not bounded from below, by constructing appropriate Liapunov functions and using the comparison method, we obtain sufficient conditions for global existence of solutions in the future and for their partial boundedness.
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42

Yang, Xiu-Yi, and Hong-Na Li. "The hypergeometric system for one-loop triangle integral." International Journal of Modern Physics A 34, no. 35 (December 20, 2019): 1950232. http://dx.doi.org/10.1142/s0217751x19502324.

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We derive the holonomic hypergeometric system for the [Formula: see text] function with two equal virtual masses, and present the expression of [Formula: see text] in hypergeometric series in corresponding convergent region. Combining the Horn’s convergence theory with Gröbner basis of polynomial ideal, one can calculate the convergence region of the corresponding multiple series concretely. Using the system given here, one can analytically continue [Formula: see text] to whole parameter space.
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43

Zarabadipour, Hassan, and Zahra Yaghoubi. "Control of a non-holonomic mobile robot system with parametric uncertainty." Tehnički glasnik 13, no. 1 (March 23, 2019): 43–50. http://dx.doi.org/10.31803/tg-20190116100550.

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In this paper, the control of a mobile robot system via a feedback linearization controller and anti-control of chaos with parametric uncertainty is researched. Anti-control is also applied to convert non-chaotic systems to chaotic ones and to create chaos dynamic. The synchronization of system errors with a chaotic gyroscope system is researched for energy reduction and performance improvement. In the other words, control effort is based on synchronizing the error system with chaos for decreasing control cost. The combination of these techniques yields high efficiency and global convergence of trajectories, even in the presence of parametric uncertainty, which has been shown by simulation. Finally, the energy of control signals is calculated and compared for showing the energy reduction.
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44

DAJCZER, MARCOS, and RUY TOJEIRO. "AN EXTENSION OF THE CLASSICAL RIBAUCOUR TRANSFORMATION." Proceedings of the London Mathematical Society 85, no. 1 (March 2002): 211–32. http://dx.doi.org/10.1112/s0024611502013552.

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We extend the notion of Ribaucour transformation from classical surface theory to the theory of holonomic submanifolds of pseudo-Riemannian space forms with arbitrary dimension and codimension, that is, submanifolds with flat normal bundle admitting a global system of principal coordinates. Bianchi gave a positive answer to the question of whether among the Ribaucour transforms of a surface with constant mean or Gaussian curvature there exist other surfaces with the same property. Our main achievement is to solve the same problem for the class of holonomic submanifolds with constant sectional curvature. 2000 Mathematical Subject Classification: 53B25, 58J72.
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45

Rehman, Fazal Ur, A. Baseer Satti, and A. Ahmed Saleem. "Continuous Stabilizing Control for a Class Of Non-holonomic systems: Brockett System Example." Journal of Vibration Testing and System Dynamics 2, no. 2 (June 2018): 167–72. http://dx.doi.org/10.5890/jvtsd.2016.06.005.

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46

Jeremic, Bojan, Radoslav Radulovic, Nemanja Zoric, and Milan Drazic. "Realizing brachistochronic planar motion of a variable mass nonholonomic mechanical system by an ideal holonomic constraint with restricted reaction." Filomat 33, no. 14 (2019): 4387–401. http://dx.doi.org/10.2298/fil1914387j.

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The paper considers realization of the brachistochronic motion of a nonholonomic mechanical system, composed of variable mass particles, by means of an ideal holonomic constraint with restricted reaction. It is assumed that the system performs planar motion in an arbitrary field of forces and that it has two degrees of freedom. In addition, the laws of the time-rate of mass variation of the particles, as well as relative velocities of the expelled and gained particles, respectively, are known. Restricted reaction of the holonomic constraint is taken for the scalar control. Applying Pontryagin?s maximum principle and singular optimal control theory, the problem of brachistochronic motion is solved as a two-point boundary value problem (TPBVP). Since the reaction of the constraint is restricted, different types of control structures are examined, from singular to totally nonsingular. The considerations are illustrated via an example.
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47

Balakin, P. D. "Determination of motion of mechanical system with non-holonomic constraints." Omsk Scientific Bulletin, no. 161 (2018): 5–7. http://dx.doi.org/10.25206/1813-8225-2018-161-5-7.

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48

Huang Wei-Li. "Inverse problem of Mei symmetry for a general holonomic system." Acta Physica Sinica 64, no. 17 (2015): 170202. http://dx.doi.org/10.7498/aps.64.170202.

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49

Wu Hui-Bin and Mei Feng-Xiang. "A gradient representation of holonomic system in the event space." Acta Physica Sinica 64, no. 23 (2015): 234501. http://dx.doi.org/10.7498/aps.64.234501.

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50

Chi, Dongpyo, Sun-Ho Choi, and Seung-Yeal Ha. "Emergent behaviors of a holonomic particle system on a sphere." Journal of Mathematical Physics 55, no. 5 (May 2014): 052703. http://dx.doi.org/10.1063/1.4878117.

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