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Journal articles on the topic 'Systeme holonome'

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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

Ito, Masahide. "Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction." Electronics 8, no. 11 (November 12, 2019): 1337. http://dx.doi.org/10.3390/electronics8111337.

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This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

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3

Cheon, Taksu, Atushi Tanaka, and Sang Wook Kim. "Exotic quantum holonomy in Hamiltonian systems." Physics Letters A 374, no. 2 (December 2009): 144–49. http://dx.doi.org/10.1016/j.physleta.2009.10.064.

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4

Stanchenko, S. V. "Non-holonomic Chaplygin systems." Journal of Applied Mathematics and Mechanics 53, no. 1 (January 1989): 11–17. http://dx.doi.org/10.1016/0021-8928(89)90126-3.

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5

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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6

WU, SIYE. "GEOMETRIC PHASES IN THE QUANTISATION OF BOSONS AND FERMIONS." Journal of the Australian Mathematical Society 90, no. 2 (April 2011): 221–35. http://dx.doi.org/10.1017/s1446788711001236.

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AbstractAfter reviewing geometric quantisation of linear bosonic and fermionic systems, we study the holonomy of the projectively flat connection on the bundle of Hilbert spaces over the space of compatible complex structures and relate it to the Maslov index and its various generalisations. We also consider bosonic and fermionic harmonic oscillators parametrised by compatible complex structures and compare Berry’s phase with the above holonomy.

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7

Asadov, Hikmat, Sevindj Abdullayeva, and Ulviya Tarverdiyeva. "Questions on Optimization of Izomorphic-Holonomic Information-Measuring Systems." Известия высших учебных заведений. Электромеханика 63, no. 6 (2020): 51–56. http://dx.doi.org/10.17213/0136-3360-2020-6-51-56.

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Questions on optimization of isomorphic-holonomic information –measuring systems, characterized by in-ternal holomorphic relation are considered. It is shown that isomorphic-holonomic property of information measuring and mechatronic systems make it possible to carry out optimization of them transforming of this task to Lagrange task where the target functional (Lagrange functional) is sum of initial target functional and integral of function of holonomic relation function with limitation imposed on it multiplied by Lagrange multi-plier. It is proved that if searched for function of holonomic relation with imposed limitation condition pro-vides for minimum (maximum) of target functional and if inegrant of initial target functional can be linearized so the function is always exists and is featured as inversed to link function upon which maximum (minimum) can be achieved.

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8

Niu, Xiaoji, You Li, Quan Zhang, Yahao Cheng, and Chuang Shi. "Observability Analysis of Non-Holonomic Constraints for Land-Vehicle Navigation Systems." Journal of Global Positioning Systems 11, no. 1 (June 30, 2012): 80–88. http://dx.doi.org/10.5081/jgps.11.1.80.

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9

Ortiz-Bobadilla, L., E. Rosales-González, and S. M. Voronin. "Extended Holonomy and Topological Invariance of Vanishing Holonomy Group." Journal of Dynamical and Control Systems 14, no. 3 (July 2008): 299–358. http://dx.doi.org/10.1007/s10883-008-9041-0.

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10

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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11

Kashiwara, Masaki, and Takahiro Kawai. "Hodge structure and holonomic systems." Proceedings of the Japan Academy, Series A, Mathematical Sciences 62, no. 1 (1986): 1–4. http://dx.doi.org/10.3792/pjaa.62.1.

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12

Chen, Jingyue, An Huang, and Bong H. Lian. "Holonomic systems for period mappings." Nuclear Physics B 898 (September 2015): 693–706. http://dx.doi.org/10.1016/j.nuclphysb.2015.07.009.

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13

Izumiya, Shyuichi, and Yasuhiro Kurokawa. "Holonomic systems of Clairaut type." Differential Geometry and its Applications 5, no. 3 (September 1995): 219–35. http://dx.doi.org/10.1016/0926-2245(95)92847-x.

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14

Moshchuk, N. K., and I. N. Sinitsyn. "On stochastic non-holonomic systems." Journal of Applied Mathematics and Mechanics 54, no. 2 (January 1990): 174–82. http://dx.doi.org/10.1016/0021-8928(90)90030-e.

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15

Balseiro, P., and J. E. Solomin. "On Generalized Non-holonomic Systems." Letters in Mathematical Physics 84, no. 1 (April 2008): 15–30. http://dx.doi.org/10.1007/s11005-008-0236-9.

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16

Ostrovskaya, S., and J. Angeles. "Nonholonomic Systems Revisited Within the Framework of Analytical Mechanics." Applied Mechanics Reviews 51, no. 7 (July 1, 1998): 415–33. http://dx.doi.org/10.1115/1.3099013.

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Nonholonomic mechanical systems are revisited. This review article focuses on Lagrangian formulations leading to a system of governing equations free of constraint forces. While eliminating the constraint forces, the number of scalar Lagrange equations is reduced to a number of independent equations lower than the original system with constraint forces. In the process of constraint-force elimination and dimension-reduction, a matrix that appears to play a relevant role in the formulation of the mathematical models of mechanical systems arises naturally. We call this matrix here the holonomy matrix. It is shown that necessary and sufficient conditions for the integrability of the constraints in Pfaffian form are readily derived using the holonomy matrix. In the same vein, a class of nonholonomic systems is identified, of current engineering relevance, that is termed quasiholonomic. Examples are included to illustrate these concepts. This review article contains 40 references.

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17

ANGELES, J., and SANGKOO LEE. "THE MODELLING OF HOLONOMIC MECHANICAL SYSTEMS USING A NATURAL ORTHOGONAL COMPLEMENT." Transactions of the Canadian Society for Mechanical Engineering 13, no. 4 (December 1989): 81–89. http://dx.doi.org/10.1139/tcsme-1989-0014.

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A computationally efficient and systematic algorithm for the modelling of constrained mechanical systems is developed and implemented in this paper. With this algorithm, the governing equations of mechanical systems comprised of rigid bodies coupled by holonomic constraints are derived by means of an orthogonal complement of the matrix of the velocity-constraint equations. The procedure is applicable to all types of holonomic mechanical systems, and it can be extended to cases including simple nonholonomic constraints. Holonomic mechanical systems having a simple Kinematic-chain structure, such as single-loop linkages and serial-type robotic manipulators, are analysed regarding the derivation of the matrix of the constraint equations and its orthogonal complement, and the computation of the constraint forces.

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18

ALVAREZ, ORLANDO, L. A. FERREIRA, and J. SÁNCHEZ-GUILLÉN. "INTEGRABLE THEORIES AND LOOP SPACES: FUNDAMENTALS, APPLICATIONS AND NEW DEVELOPMENTS." International Journal of Modern Physics A 24, no. 10 (April 20, 2009): 1825–88. http://dx.doi.org/10.1142/s0217751x09043419.

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We review our proposal to generalize the standard two-dimensional flatness construction of Lax–Zakharov–Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is Abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four-dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume-preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang–Mills theories are summarized. We also discuss other possibilities that have not yet been explored.

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19

Urbantke, H. "Two‐level quantum systems: States, phases, and holonomy." American Journal of Physics 59, no. 6 (June 1991): 503–9. http://dx.doi.org/10.1119/1.16809.

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20

Nagy, P. T. "New Developments in Holonomy Theory of Differentiable Systems." Journal of Mathematical Sciences 218, no. 6 (September 29, 2016): 808–12. http://dx.doi.org/10.1007/s10958-016-3068-7.

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21

Udwadia, Firdaus E., and Phailaung Phohomsiri. "Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2071 (February 28, 2006): 2097–117. http://dx.doi.org/10.1098/rspa.2006.1662.

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We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D'Alembert's principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.

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22

Egri-Nagy, Attila, and Chrystopher L. Nehaniv. "Hierarchical Coordinate Systems for Understanding Complexity and its Evolution, with Applications to Genetic Regulatory Networks." Artificial Life 14, no. 3 (July 2008): 299–312. http://dx.doi.org/10.1162/artl.2008.14.3.14305.

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Beyond complexity measures, sometimes it is worthwhile in addition to investigate how complexity changes structurally, especially in artificial systems where we have complete knowledge about the evolutionary process. Hierarchical decomposition is a useful way of assessing structural complexity changes of organisms modeled as automata, and we show how recently developed computational tools can be used for this purpose, by computing holonomy decompositions and holonomy complexity. To gain insight into the evolution of complexity, we investigate the smoothness of the landscape structure of complexity under minimal transitions. As a proof of concept, we illustrate how the hierarchical complexity analysis reveals symmetries and irreversible structure in biological networks by applying the methods to the lac operon mechanism in the genetic regulatory network of Escherichia coli.

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23

Coutinho, F. A. B., and M. Amaku. "A note on nonholonomic systems." Revista Brasileira de Ensino de Física 31, no. 2 (June 2009): 2702.1–2702.2. http://dx.doi.org/10.1590/s1806-11172009000200017.

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24

Lemos, Nivaldo A. "Breakdown of the connection between symmetries and conservation laws for semiholonomic systems." American Journal of Physics 90, no. 3 (March 2022): 221–24. http://dx.doi.org/10.1119/5.0067183.

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Integrable velocity-dependent constraints are said to be semiholonomic. For good reasons, holonomic and semiholonomic constraints are thought to be indistinguishable in Lagrangian mechanics. This well-founded belief notwithstanding, here we show by means of an example and a broad analysis that the connection between symmetries and conservation laws, which holds for holonomic systems, is not valid in general for systems subject to semiholonomic constraints.

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25

Batlle, J. A., and A. Barjau. "Holonomy in mobile robots." Robotics and Autonomous Systems 57, no. 4 (April 2009): 433–40. http://dx.doi.org/10.1016/j.robot.2008.06.001.

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26

Saito, Mutsumi, Bernd Sturmfels, and Nobuki Takayama. "Gröbner deformations of regular holonomic systems." Proceedings of the Japan Academy, Series A, Mathematical Sciences 74, no. 7 (1998): 111–13. http://dx.doi.org/10.3792/pjaa.74.111.

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27

TAKAHASHI, Masatomo. "Holonomic systems of general Clairaut type." Hokkaido Mathematical Journal 34, no. 1 (February 2005): 247–63. http://dx.doi.org/10.14492/hokmj/1285766207.

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28

Xue-Jun, Xu, Qin Mao-Chang, and Mei Feng-Xiang. "Unified symmetry of holonomic mechanical systems." Chinese Physics 14, no. 7 (June 23, 2005): 1287–89. http://dx.doi.org/10.1088/1009-1963/14/7/003.

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29

Espindola, O., M. L. Espindola, L. J. Negri, and N. L. Teixeira. "Hamiltonisation of classical non-holonomic systems." Journal of Physics A: Mathematical and General 20, no. 7 (May 11, 1987): 1713–17. http://dx.doi.org/10.1088/0305-4470/20/7/017.

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30

Jurdjevic, V. "The Geometry of Non Holonomic Systems." IFAC Proceedings Volumes 25, no. 13 (June 1992): 89–94. http://dx.doi.org/10.1016/s1474-6670(17)52263-6.

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31

Moauro, Vinicio. "A stability problem for holonomic systems." Annali di Matematica Pura ed Applicata 139, no. 1 (December 1985): 227–35. http://dx.doi.org/10.1007/bf01766856.

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32

Langer, F. Dieter, H. Hemami, and D. B. Brown. "Constraint forces in holonomic mechanical systems." Computer Methods in Applied Mechanics and Engineering 62, no. 3 (June 1987): 255–74. http://dx.doi.org/10.1016/0045-7825(87)90062-4.

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33

Andreev, Yu M., and O. K. Morachkovskii. "Dynamics of Holonomic Rigid-Body Systems." International Applied Mechanics 41, no. 7 (July 2005): 817–24. http://dx.doi.org/10.1007/s10778-005-0150-0.

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34

EL-Nabulsi, Ahmad Rami. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems." Chaos, Solitons & Fractals 42, no. 1 (October 2009): 52–61. http://dx.doi.org/10.1016/j.chaos.2008.10.022.

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35

Prykarpatskyy, Yarema A. "Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations." Symmetry 13, no. 6 (June 16, 2021): 1077. http://dx.doi.org/10.3390/sym13061077.

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Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

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36

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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37

Poznanski, Roman, Eda Alemdar, Cacha Lleuvelyn, Valeriy Sbitnev, and Erkki Brandas. "Journal of Multiscale Neuroscience." Journal of Multiscale Neuroscience 1, no. 2 (October 28, 2022): 109–33. http://dx.doi.org/10.56280/1546792195.

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information based on an inter-cerebral superfast, spontaneous information pathway involving protein-protein interactions. Protons are convenient quantum objects for transferring bit units in a complex water medium like the brain. The phonon-polariton interaction in such a medium adds informational complexity involving complex protein interactions that are essential for the superfluid-like highway to enable the consciousness process to penetrate brain regions due to different regulated gene sets as opposed to single region-specific genes. Protein pathways in the cerebral cortices are connected in a single network of thousands of proteins. To understand the role of inter-cerebral communication, we postulate protonic currents in interfacial water crystal lattices result from phonon-polariton vibrations, which can lead in the presence of an electromagnetic field, to ultra-rapid communication where thermo-qubits, physical feelings, and protons that are convenient quantum objects for transferring bit units in a complex water medium. The relative equality between the frequencies of thermal oscillations due to the energy of the quasi-protonic movement about a closed loop and the frequencies of electromagnetic oscillations confirms the existence of quasi-polaritons. Phonon-polaritons are electromagnetic waves coupled to lattice vibrational modes. Still, when generated specifically by protons, they are referred to as phonon-coupled quasi-particles, i.e., providing a coupling with vibrational motions. We start from quasiparticles and move up the scale to biomolecular communication in subcellular, cellular and neuronal structures, leading to the negentropic entanglement of multiscale ‘bits’ of information. Espousing quantum potential chemistry, the interdependence of intrinsic information on the negative gain in the steady-state represents the mesoscopic aggregate of the microscopic random quantum-thermal fluctuations expressed through a negentropically derived, temperature-dependent, dissipative quantum potential energy. The latter depends on the time derivative of the spread function and temperature, which fundamentally explains the holonomic brain theory.

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38

Feigin, Misha V., and Alexander P. Veselov. "$\vee$ -Systems, Holonomy Lie Algebras, and Logarithmic Vector Fields." International Mathematics Research Notices 2018, no. 7 (January 8, 2017): 2070–98. http://dx.doi.org/10.1093/imrn/rnw289.

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Abstract It is shown that the description of certain class of representations of the holonomy Lie algebra $\mathfrak g_{\Delta}$ associated with hyperplane arrangement $\Delta$ is essentially equivalent to the classification of $\vee$-systems associated with $\Delta.$ The flat sections of the corresponding $\vee$-connection can be interpreted as vector fields, which are both logarithmic and gradient. We conjecture that the hyperplane arrangement of any $\vee$-system is free in Saito's sense and show this for all known $\vee$-systems and for a special class of $\vee$-systems called harmonic, which includes all Coxeter systems. In the irreducible Coxeter case the potentials of the corresponding gradient vector fields turn out to be Saito flat coordinates, or their one-parameter deformations. We give formulas for these deformations as well as for the potentials of the classical families of harmonic $\vee$-systems.

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39

Wang, Jian, Ting Wang, Chen Yao, Xiaofan Li, and Chengdong Wu. "Active Tension Control for WT Wheelchair Robot by Using a Novel Control Law for Holonomic or Nonholonomic Systems." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/236515.

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Interactional characteristics between WT wheelchair robot and stair environment are analyzed, and possible patterns of WT wheelchair robot during the stair-climbing process are summarized, with the criteria of the wheelchair robot for determining the pattern proposed. Aiming at WT wheelchair robot's complicated mechanism with holonomic constraints and combined with the computed torque method, a novel control law that is called active tension control is presented for holonomic or nonholonomic robotic systems, by which the wheelchair robot with a holonomic or nonholonomic mechanism can track the reference input of the constraint forces of holonomic or nonholonomic constraints as well as tracking the reference input of the generalized coordinate of each joint. A stateflow module of Matlab is used to simulate the entire stair-climbing process for WT wheelchair robot. A comparison of output curve with the reference input curve of each joint is made, with the effectiveness of the presented control law verified.

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40

Popescu, Marcela, and Paul Popescu. "Noether Invariants for Nonholonomic Systems." Symmetry 13, no. 4 (April 10, 2021): 641. http://dx.doi.org/10.3390/sym13040641.

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The aim of this paper is to construct Noether invariants for Lagrangian non-holonomic dynamics with affine or nonlinear constraints, considered to be adapted to a foliation on the base manifold. A set of illustrative examples is given, including linear and nonlinear Appell mechanical systems.

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41

Biswas, Indranil, and Niels Leth Gammelgaard. "Vassiliev invariants from symmetric spaces." Journal of Knot Theory and Its Ramifications 25, no. 10 (September 2016): 1650055. http://dx.doi.org/10.1142/s0218216516500553.

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We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are exactly characterized by having the symmetries of the Riemann curvature tensor.

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42

Nakamura, Yoshihiko. "Non-holonomic Robot Systems. Part 5. Motion Control under Dynamical Non-holonomic Constraints." Journal of the Robotics Society of Japan 12, no. 2 (1994): 231–39. http://dx.doi.org/10.7210/jrsj.12.231.

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43

Terze, Zdravko, and Joris Naudet. "Structure of optimized generalized coordinates partitioned vectors for holonomic and non-holonomic systems." Multibody System Dynamics 24, no. 2 (March 16, 2010): 203–18. http://dx.doi.org/10.1007/s11044-010-9195-x.

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44

Gripaios, Ben, and Joseph Tooby-Smith. "Inverse Higgs phenomena as duals of holonomic constraints." Journal of Physics A: Mathematical and Theoretical 55, no. 9 (February 7, 2022): 095401. http://dx.doi.org/10.1088/1751-8121/ac4c66.

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Abstract The inverse Higgs phenomenon, which plays an important rôle in physical systems with Goldstone bosons (such as the phonons in a crystal) involves nonholonomic mechanical constraints. By formulating field theories with symmetries and constraints in a general way using the language of differential geometry, we show that many examples of constraints in inverse Higgs phenomena fall into a special class, which we call coholonomic constraints, that are dual (in the sense of category theory) to holonomic constraints. Just as for holonomic constraints, systems with coholonomic constraints are equivalent to unconstrained systems (whose degrees of freedom are known as essential Goldstone bosons), making it easier to study their consistency and dynamics. The remaining examples of inverse Higgs phenomena in the literature require the dual of a slight generalisation of a holonomic constraint, which we call (co)meronomic. Our formalism simplifies and clarifies the many ad hoc assumptions and constructions present in the literature. In particular, it identifies which are necessary and which are merely convenient. It also opens the way to studying much more general dynamical examples, including systems which have no well-defined notion of a target space.

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45

Ge Wei-Kuan, Xue Yun, and Lou Zhi-Mei. "Generalized gradient representation of holonomic mechanical systems." Acta Physica Sinica 63, no. 11 (2014): 110202. http://dx.doi.org/10.7498/aps.63.110202.

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46

D’Agnolo, Andrea, and Masaki Kashiwara. "On a reconstruction theorem for holonomic systems." Proceedings of the Japan Academy, Series A, Mathematical Sciences 88, no. 10 (October 2012): 178–83. http://dx.doi.org/10.3792/pjaa.88.178.

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47

Consolini, Luca, and Manfredi Maggiore. "Virtual Holonomic Constraints for Euler-Lagrange Systems." IFAC Proceedings Volumes 43, no. 14 (September 2010): 1193–98. http://dx.doi.org/10.3182/20100901-3-it-2016.00107.

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Ge Wei-Kuan and Zhang Yi. "Lie-form invariance of holonomic mechanical systems." Acta Physica Sinica 54, no. 11 (2005): 4985. http://dx.doi.org/10.7498/aps.54.4985.

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Maggiore, Manfredi, and Luca Consolini. "Virtual Holonomic Constraints for Euler–Lagrange Systems." IEEE Transactions on Automatic Control 58, no. 4 (April 2013): 1001–8. http://dx.doi.org/10.1109/tac.2012.2215538.

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Mukherjee, R., and R. C. Rosenberg. "Gyroscopic Coupling in Holonomic Lagrangian Dynamical Systems." Journal of Applied Mechanics 66, no. 2 (June 1, 1999): 552–56. http://dx.doi.org/10.1115/1.2791084.

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