Relevant bibliographies by topics / Action-Angle variables

Academic literature on the topic 'Action-Angle variables'

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Published: 20 April 2024

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Journal articles on the topic "Action-Angle variables"

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Spergel, David N. "Natural Action–Angle Variables." Symposium - International Astronomical Union 127 (1987): 483–84. http://dx.doi.org/10.1017/s0074180900185857.

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Since galaxies are collisionless relaxed systems, actions are an extremely useful tool for understanding their dynamics. There are many potential applications of actions: (1) When orbits in an N-body simulation are characterized by their actions, the six dimensional distribution function, can be reduced to a more tractable three dimensional function, f(J). (2) Actions are adiabatic invariants, and thus are useful for studying slowly evolving systems. Binney, May and Ostriker (1986) have applied this technique to study the response of the spheroid to the disc. (3) the spectral decomposition of an orbit can be used to help generate self–consistent galaxy models (Spergel 1987).
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Bates, Larry, and Jedrzej Śniatycki. "On action-angle variables." Archive for Rational Mechanics and Analysis 120, no. 4 (December 1992): 337–43. http://dx.doi.org/10.1007/bf00380319.

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YEON*, Kyu Hwang, and Eun Ji LIM. "Quantum Action-angle Variables." New Physics: Sae Mulli 63, no. 5 (May 31, 2013): 524–30. http://dx.doi.org/10.3938/npsm.63.524.

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Llave, R. de la, A. González, À. Jorba, and J. Villanueva. "KAM theory without action-angle variables." Nonlinearity 18, no. 2 (January 22, 2005): 855–95. http://dx.doi.org/10.1088/0951-7715/18/2/020.

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Lahiri, Abhijit, Gautam Ghosh, and T. K. Kar. "Action-angle variables in quantum mechanics." Physics Letters A 238, no. 4-5 (February 1998): 239–43. http://dx.doi.org/10.1016/s0375-9601(97)00926-2.

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Chavanis, Pierre-Henri. "Kinetic theory with angle–action variables." Physica A: Statistical Mechanics and its Applications 377, no. 2 (April 2007): 469–86. http://dx.doi.org/10.1016/j.physa.2006.11.078.

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Mahajan, S. M., and C. Y. Chen. "Plasma kinetic theory in action-angle variables." Physics of Fluids 28, no. 12 (1985): 3538. http://dx.doi.org/10.1063/1.865308.

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Bellucci, Stefano, Armen Nersessian, Armen Saghatelian, and Vahagn Yeghikyan. "Quantum Ring Models and Action-Angle Variables." Journal of Computational and Theoretical Nanoscience 8, no. 4 (April 1, 2011): 769–75. http://dx.doi.org/10.1166/jctn.2011.1751.

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Hakobyan, T., O. Lechtenfeld, A. Nersessian, A. Saghatelian, and V. Yeghikyan. "Action-angle variables and novel superintegrable systems." Physics of Particles and Nuclei 43, no. 5 (September 2012): 577–82. http://dx.doi.org/10.1134/s1063779612050152.

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Khein, Alexander, and D. F. Nelson. "Hannay angle study of the Foucault pendulum in action‐angle variables." American Journal of Physics 61, no. 2 (February 1993): 170–74. http://dx.doi.org/10.1119/1.17332.

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Dissertations / Theses on the topic "Action-Angle variables"

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Boucetta, Mohamed. "Modèles locaux d'actions hamiltoniennes et variables action-angle." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376032479.

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Dehouck, Victor. "Invariance Adiabatique dans les Mouvements Rythmiques Volontaires Humains." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCK066.

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Les mouvements humains sont toujours complexes. Même une tâche simple comme prendre un verre d'eau implique de nombreux degrés de liberté i.e., différents groupes de muscles, plusieurs articulations et un nombre infini de trajectoires possible pour le bras. Néanmoins, les mouvements sont facilement disponibles aux sujets sains et semble être naturellement optimisé par le système nerveux central. Cela est souvent modélisé par la minimisation d'un paramètre donné du système, tel que l'énergie ou l'à-coup, qui semblent être des candidats naturels. Malheureusement, ces approches sont souvent limitées dans leur portée et ne peuvent pas décrire les mouvements périodiques dans des environnements changeant dans le temps. Dans de tels systèmes, les invariants adiabatiques sont des observables pertinentes issues de la mécanique hamiltonienne. L'objectif de cette thèse de doctorat est d'étudier le rôle et l'utilisation des invariants adiabatiques dans le contrôle moteur humain. Pour ce faire, nous avons réalisé une série d'expériences. Tout d'abord, nous les avons étudiées en tant que contrainte pour la stabilité globale de la marche, même lorsqu'elle est exposée à une tâche altérant la variabilité, telle que le maintien d'un rythme dicté par un métronome. Ensuite, nous avons utilisé des résultats récents en physique pour évaluer la variabilité inhérente à la marche à longue distance en tant que phénomène de diffusion de la distribution des invariants adiabatiques. Enfin, nous les avons explorés dans des environnements temporels changeants, notamment en modifiant la "gravité" à la fois dans une centrifugeuse et dans un contexte de vol parabolique, où ils semblent être des quantités pertinentes pour montrer les changements dans les stratégies motrices. Les différents résultats de cette thèse indiquent que les invariants adiabatiques révèlent des contraintes génériques cachées affectant les mouvements humains périodiques
Human motion is inherently complex. Even an ordinary task like lifting a glass of water involves many degrees of freedom i.e., different muscle groups, multiple joints and an infinite number of trajectories for the arm. Nevertheless, motion is readily available to healthy subjects, and seems to be naturally optimized by the central nervous system. This is often modelized as the minimization of a given parameter of the system e.g., energy or jerk, which appear as natural candidates. Unfortunately, these approaches are often limited in their scopes, and cannot describe periodic motion in time-changing environments. In such systems, adiabatic invariants are relevant observables originating from Hamiltonian mechanics. The aim of this doctoral dissertation is to investigate the role and use of adiabatic invariants in human motor control. This was done in a series of experiments. First, we studied them as a constraint for the global stability of gait, even when exposed to a variability-altering task, such as metronome keeping. Then, we used recent results in physics to assess the inherent variability of long-range walking as a diffusion phenomenon of the distribution of adiabatic invariants. Finally, we explored them in time-changing environments, specifically by altering “gravity” both in a centrifuge and a parabolic flight context, where they seem to be relevant quantities to show changes in motor strategies. The different findings in this dissertation point to adiabatic invariants revealing generic hidden constraints affecting periodic human motion
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Horsin, Romain. "Comportement en temps long d'équations de type Vlasov : études mathématiques et numériques." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S062/document.

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Cette thèse porte sur le comportement en temps long de solutions d’équations de type Vlasov, principalement le modèle Vlasov-HMF. On s’intéresse en particulier au phénomène d’amortissement Landau, prouvé mathématiquement dans divers cadres, pour plusieurs équations de type Vlasov, comme l’équation de Vlasov-Poisson ou le modèle Vlasov-HMF, et présentant certaines analogies avec le phénomène d’amortissement non visqueux pour l’équation d’Euler 2D. Les résultats qui y sont décrits sont les suivants. Le premier est un théorème d’amortissement Landau pour des solutions numériques du modèle Vlasov-HMF, obtenues par discrétisation en temps de ce dernier via des méthodes de splitting. Nous prouvons en outre la convergence des schémas numériques. Le second est un théorème d’amortissment Landau pour des solutions du modéle Vlasov-HMF linéarisé autour d’états stationnaires inhomogènes. Ce théorème est accompagné de nombreuses simulations numériques destinées à étudier numériquement le cas non-linéaire, et semblant mettre en lumière de nouveaux phénomènes. Enfin, le dernier résultat porte sur la discrétisation en temps de l’équation d’Euler 2D par un intégrateur de Crouch-Grossman symplectique. Nous prouvons la convergence du schéma
This thesis concerns the long time behavior of certain Vlasov equations, mainly the Vlasov- HMF model. We are in particular interested in the celebrated phenomenon of Landau damp- ing, proved mathematically in various frameworks, foar several Vlasov equations, such as the Vlasov-Poisson equation or the Vlasov-HMF model, and exhibiting certain analogies with the inviscid damping phenomenon for the 2D Euler equation. The results described in the document are the following.The first one is a Landau damping theorem for numerical solutions of the Vlasov-HMF model, constructed by means of time-discretizations by splitting methods. We prove more- over the convergence of the schemes. The second result is a Landau damping theorem for solutions of the Vlasov-HMF model linearized around inhomogeneous stationary states. We provide moreover a quite large amount of numerical simulations, which are designed to study numerically the nonlinear case, and which seem to show new phenomenons. The last result is the convergence of a scheme that discretizes in time the 2D Euler equation by means of a symplectic Crouch-Grossmann integrator
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Papaphilippou, Yannis. "APPLICATION DE LA METHODE D'ANALYSE EN FREQUENCE EN DYNAMIQUE GALACTIQUE." Phd thesis, Université Paris-Diderot - Paris VII, 1997. http://tel.archives-ouvertes.fr/tel-00836476.

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Dans le but de clarifier les aspects dynamiques des modèles galactiques triaxiaux, le potentiel logarithmique est étudié a travers la méthode d'analyse en fréquence. Les caractéristiques dynamiques principales du système sont présentées en utilisant le formalisme hamiltonien approprié. Afin de comparer cette nouvelle approche avec des études précédentes, la méthode est appliquée a la version axisymétrique du potentiel. La précision de la méthode est démontrée a travers des techniques de perturbation et des transformations numériques en variables action-angle. En outre, la construction des applications fréquence pour plusieurs valeurs du paramètre de perturbation permet de fournir une vision globale de la dynamique du potentiel plan. Les zones chaotiques, les résonances importantes ainsi que les orbites périodiques sont détectées. La méthode est appliquée ensuite a la version tridimensionnelle du potentiel logarithmique. Les approximations quasi-périodiques fournies par la méthode permettent de clarifier la dynamique des types d'orbites principales et leur connexion avec des perturbations du hamiltonien général. Tous les détails fins de la dynamique, qui sont associés a l'addition du troisième degré de liberté, sont représentés dans les applications fréquence complètes, des images instantanées du réseau d'Arnold (''Arnol'd web'') du système. Ainsi, nous pouvons visualiser l'étendu des zones chaotiques et l'influence des lignes résonantes dans l'espace physique du système. Cette approche révèle plusieurs caractéristiques dynamiques inconnues des potentiels galactiques triaxiaux et indique que le chaos doit être une caractéristique importante des configurations triaxiales. Nous discutons finalement l'influence de ces résultats sur la construction des modèles galactiques auto-consistants.
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Khorev, Alexeĭ Borisovich. "The concept of approximate action-angle variables for nonintegrable Hamiltonian dynamics." Phd thesis, 2002. http://hdl.handle.net/1885/148601.

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Books on the topic "Action-Angle variables"

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Mann, Peter. Poisson Brackets & Angular Momentum. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0017.

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This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.
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Mann, Peter. The Structure of Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0023.

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This chapter introduces the reader to canonical perturbation theory as a tool for studying near-integrable systems. Many problems in physics and chemistry do not have exact analytical solutions; these systems are in direct opposition to integrable systems and action-angle variables. The chapter starts by considering tiny perturbations to integrable Hamiltonians. Poincaré in 1893 claimed this was the fundamental question of classical mechanics and, fittingly, Hamilton–Jacobi theory is the starting point. The chapter develops Poincaré’s fundamental equation as well as Delaunay’s small divisor problem. Resonant, near–resonant and non-resonant tori are investigated in the context of Poincaré’s theorem and KAM theory is described in detail. Chaos and Poincaré maps are presented before discussing determinism, deterministic chaos and Laplace’s demon.
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Book chapters on the topic "Action-Angle variables"

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Dittrich, W., and Martin Reutera. "Action-Angle Variables." In Classical and Quantum Dynamics, 83–104. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56430-7_8.

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Dittrich, Walter, and Martin Reuter. "Action-Angle Variables." In Classical and Quantum Dynamics, 93–117. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36786-2_8.

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Dittrich, Walter, and Martin Reuter. "Action-Angle Variables." In Classical and Quantum Dynamics, 75–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-97465-6_7.

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Dittrich, Walter, and Martin Reuter. "Action-Angle Variables." In Classical and Quantum Dynamics, 93–117. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58298-6_8.

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Dittrich, Walter, and Martin Reuter. "Action-Angle Variables." In Classical and Quantum Dynamics, 93–117. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-21677-5_8.

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Dittrich, Walter, and Martin Reuter. "Action-Angle Variables." In Classical and Quantum Dynamics, 75–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-97921-7_7.

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Spergel, David N. "Natural Action-Angle Variables." In Structure and Dynamics of Elliptical Galaxies, 483–84. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3971-4_84.

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Oevel, G., B. Fuchssteiner, and M. Błaszak. "Action-Angle Variables and Asymptotic Data." In Nonlinear Evolution Equations and Dynamical Systems, 123–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-84039-5_22.

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Stupakov, Gennady, and Gregory Penn. "Action-Angle Variables and Liouville’s Theorem." In Graduate Texts in Physics, 31–45. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90188-6_3.

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Stupakov, Gennady, and Gregory Penn. "Action-Angle Variables for Betatron Oscillations." In Graduate Texts in Physics, 87–94. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90188-6_7.

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Conference papers on the topic "Action-Angle variables"

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Visinescu, Mihai. "Complete integrability of geodesics in toric Sasaki-Einstein space T 1,1 and action-angle variables." In HIGH ENERGY GAMMA-RAY ASTRONOMY: 6th International Meeting on High Energy Gamma-Ray Astronomy. Author(s), 2017. http://dx.doi.org/10.1063/1.4972349.

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Renno, Jamil M. "Inverse Dynamics Based Fuzzy Logic Controller for a Single-Link Flexible Manipulator." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79028.

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This paper presents a novel method for an inverse dynamics based fuzzy logic controller (FLC) of a single-link flexible manipulator. The control action is distributed between two FLCs: a joint angle controller and a tip controller. A method for varying the ranges of the variables of the two controllers as a function of the motion parameters and the inverse dynamics of the system is presented. Simulation results show that the joint trajectory tracking is accomplished and the residual vibration of the flexible link is suppressed.
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Kulshreshtha, Digvijay B., and S. A. Channiwala. "Flow in Atomizers: Influence of Different Parameters on the Performance Characteristics of Plain Orifice Atomizer and Pressure Swirl Atomizer of a Fuel Injection System of Gas Turbine Combustor." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77122.

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The atomization process is essentially one in which bulk liquid is converted into small drops. Basically, it can be considered as a disruption of the consolidating influence of surface tension by the action of internal and external forces. In the absence of such disruptive forces, surface tension tends to pull the liquid into the form of a sphere, since this has the minimum surface energy. Liquid viscosity exerts a stabilizing influence by opposing any change in system geometry. On the other end, aerodynamic forces acting on the liquid surface may promote the disruption process by applying an external distortion force to the bulk liquid. Breakup occurs when the magnitude of the disruptive force just exceeds the consolidating surface tension force. In twin fluid atomizers of the air-blast type and air assist type, atomization and spray dispersion tend to be dominated by air momentum forces, with hydrodynamic processes playing only a secondary role. With pressure swirl nozzles, the internal flow characteristics are of primary importance, because they govern the thickness and uniformity of the annular liquid film formed in the final discharge orifice as well as the relative magnitude of the axial and tangential components of velocity of this film. It is therefore of great practical interest to examine the interrelationships that exist between internal flow characteristics, nozzle design variables, and important spray features such as cone angle and mean drop size. The various equations that have been derived for nozzle discharge coefficient are discussed because this coefficient not only affects the flow rate of any given nozzle but also can be used to calculate its velocity coefficients and spray cone angle. Consideration is also given to the complex flow situations that arise on the surface of a rotating cup or disk. These flow characteristics are of basic importance to the successful operation of atomizers, because they exercise a controlling influence on the nature of the atomization process, the quality of atomization, and distribution of drop sizes in the spray. For plain orifice atomizers, the key geometrical variables are the orifice length and diameter. Final orifice diameter is of prime importance for pressure swirl atomizers. The absence of any theoretical treatment of the atomization process has led to the evolution of empirical equations to express the relationship between the mean drop size in a spray and the variable liquid properties. This paper includes the study of different parameters that affect the flow in plain orifice and pressure swirl atomizers. The paper also includes the performance characteristics of plain orifice and pressure swirl atomizers.
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Butcher, Eric A., and S. C. Sinha. "Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4107.

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Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.
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Kwon, Hyun Jung, Yujiang Xiang, Salam Rahmatalla, R. Timothy Marler, Karim Abdel-Malek, and Jasbir S. Arora. "Optimization-Based Digital Human Dynamics: Santos™ Walking Backwards." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35616.

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An objective of this study is to simulate the backward walking motion of a full-body digital human model. The model consists of 55 degree of freedom – 6 degrees of freedom for global translation and rotation and 49 degrees of freedom representing the kinematics of the entire body. The resultant action of all the muscles at a joint is represented by the torque for each degree of freedom. The torques and angles at a joint are treated as unknowns in the optimization problem. The B-spline interpolation is used to represent the time histories of the joint angles and the well-established robotics formulation of the Denavit-Hartenberg method is used for kinematics analysis of the mechanical system. The recursive Lagrangian formulation is used to develop the equations of motion, and was chosen because of its known computational efficiency. The backwards walking problem is formulated as a nonlinear optimization problem. The control points of the B-splines for the joint angle profiles are treated as the design variables. For the performance measure, total dynamic effort that is represented as the integral of the sum of the squares of all the joint torques is minimized using a sequential quadratic programming algorithm. The solution is simulated in the Santos™ environment. Results of the optimization problem are the torque and joint angle profiles. The torques at the key joints and the ground reaction forces are compared to those for the forward walk in order to study the differences between the two walking patterns. Simulation results are approximately validated with the experimental data which is motion captured in the VSR Lab at the University of Iowa.
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Gatapova, Elizaveta Ya, Vladimir V. Kuznetsov, Oleg A. Kabov, and Jean-Claude Legros. "Annular Liquid Film Flow Under Local Heating in Microchannel." In ASME 3rd International Conference on Microchannels and Minichannels. ASMEDC, 2005. http://dx.doi.org/10.1115/icmm2005-75253.

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In our previous investigations the formation of liquid bump of locally heated laminar liquid film with co-current gas flow was obtained [1,2]. The evaporation of liquid was left out of account. Heat transfer to the gas phase was approximately specified by a constant Biot number [2,3]. The aim of this work is an investigation of the evaporation effect, the hydrodynamics and the heat transfer of liquid film flow in a channel 0.2–1 mm height. The 2-D model of locally heated liquid film moving under gravity and the action of co-current gas flow with low viscosity in a channel are considered. The channel can be inclined at an angle with respect to horizon. It is supposed that the height of the channel is much less than its width. Surface tension is assumed to depend on temperature. The velocity profiles for gas and liquid regions are found from problem of joint motion of isothermal non-deformable liquid film and gas flow. Using the findings the joint solution of heat transfer and diffusion problem with corresponding boundary condition is calculated. Having the temperature field in the whole of liquid and gas flow region we find a local heat transfer coefficient on the gas-liquid interface and Biot number as a function of flow parameters and spatial variables.
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Raghavan, Madhusudan. "Kinematics of the Full-Toroidal Traction Drive Variator." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/mech-14170.

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Abstract We present a geometric derivation of the kinematics of the steering action and the roller displacement in a full-toroidal continuously variable traction drive variator. In particular, expressions relating the inclination of the roller to its displacement for designs incorporating a caster angle are derived. These results are useful in the design of the control system for the variator.
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Balabina, Tat'yana, Mariya Karelina, and Aleksey Mamaev. "THE INFLUENCE OF THE LENGTHS OF THE LINKS OF THE HINGED FOUR-LINK ON THE ANGLE OF HEIGHT, RETURN ANGLE AND RELATIVE DISPLACEMENT OF LINKS CONNECTED BY THE ELASTIC ELEMENT DURING THE OUTPUT LINK STABILITY." In PROBLEMS OF APPLIED MECHANICS. Bryansk State Technical University, 2020. http://dx.doi.org/10.30987/conferencearticle_5fd1ed03b024e0.49570399.

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Toothed-lever and cam-toothed-lever mechanisms are widely used in technological equipment of automatic and semi-automatic action to convert the one-way rotational motion of the input link into one-way rotary motion of the output link with periodic stops. To ensure periodic rotation with a precise fixed length, an elastic element with a preload of two-sided action is introduced into the mechanism, as a result of which the mechanism has a variable structure. Compared to other mechanisms of periodic rotation, in gear-link mechanisms there is a wide possibility of influencing the function of the position of the output link, the angle of reverse rotation and the relative displacements of the links connected to each other by an elastic element by changing the lengths of the links of the basic hinged four-link
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Meng, Qingkai, Zhifang Ke, Wei Wei, Molei Zhao, Jinghan Tu, and Qingdong Yan. "Study on the Transient Dynamic Characteristics of the Pitch-Regulated Device for Coaxilcopter Under Aerodynamic Loads." In ASME Turbo Expo 2023: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/gt2023-103937.

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Abstract Coaxilcopter with variable rotor space can dynamically adjust the parameters such as the angle of attack of blades through the pitch-regulated device, so it can adjust and change flight attitude. However, both the rotor aerodynamics and the structure of the pitch-regulated device are complex, and some of the forces generated by the rotor will act on such device in the form of a hinge moment, which would affect the realiablity of the variable pitch-regulated device and the whole craft. Therefore, a coaxilcopter with a pitch-regulated device is designed, and the finite element numerical simulation method is promoted to calculate and analyze the transient aerodynamic loads of the rotor under different rotor spaces and unbalanced angle between blades. The hinge moment load results are further applied to the variable pitch-regulated device, and the dynamic characteristics of the variable pitch-regulated device under the action of hinge moment are further studied. The results show that when the unbalanced angle between the left and right blade would lead to the increase of the hinge moment of both blade, and with the increase of rotor speed, the hinge moment of both the left and right blades gradually increases; When the hinge moment is applied to the variable pitch-regulated device, the steering gear load of the lower rotor is 1.57 times that of the rotor steering gear when the propeller spacing is 0.1R (R is rotor radius); When the propeller spacing is 1.2R, the actuator load of the upper rotor is 6%∼12% different from that of the single rotor mode, indicating that the influence of propeller spacing on the upper rotor is negligible at 1.2R, but the actuator load of the lower rotor is about 35% different from that of the single rotor mode, which has a significant influence. It also reveals that the aerodynamic interaction between rotors would affect the hinge moment, it provides a basis for the design of variable pitch-regulated device, and provides a reference for the variable pitch control strategy of aerodynamic performance, which has practical engineering significance.
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10

Carneiro, J. Falca˜o, and F. Gomes de Almeida. "VSC Approach Angle Based Boundary Layer Thickness: A New Variation Law and Its Stability Proof." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-5948.

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A major drawback on the use of sliding mode controllers is their inherent intense control activity. A usual strategy to cope with this problem is to use a boundary layer around the switching surface. The boundary layer thickness choice is based on a compromise between smoothness in the control action and tracking error. Since this compromise may be difficult to achieve, several boundary layer thickness variation laws (BLTVL) have been proposed in literature. In a recent study [1] an interesting BLTVL was proposed, based on the approach angle of the state to the switching surface. Although innovative, that study does not provide a proof of the stability of the controller. Furthermore, the BLTVL definition varies according to the system order and sliding surface definition. This paper extends the work done in [1] by presenting a new BLTVL based on a generalised definition of the approach angle that can be applied to systems of any order using any sliding surface. Furthermore, an innovative stability proof of a variable structure controller (VSC) using the new BLTVL is provided. Experimental results obtained in a servopneumatic system validate the usefulness of this approach.
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Reports on the topic "Action-Angle variables"

1

Reiman, A. H., and N. Pomphrey. Computation of magnetic coordinates and action-angle variables. Office of Scientific and Technical Information (OSTI), October 1989. http://dx.doi.org/10.2172/5663222.

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2

Morrison, P. J., and D. Pfirsch. Dielectric energy versus plasma energy, and Hamiltonian action-angle variables for the Vlasov equation. Office of Scientific and Technical Information (OSTI), April 1992. http://dx.doi.org/10.2172/10147775.

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3

Morrison, P. J., and D. Pfirsch. Dielectric energy versus plasma energy, and Hamiltonian action-angle variables for the Vlasov equation. Office of Scientific and Technical Information (OSTI), April 1992. http://dx.doi.org/10.2172/5064541.

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