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Relevant bibliographies by topics / Variables action-Angles

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Journal articles

Academic literature on the topic 'Variables action-Angles'

Author: Grafiati

Published: 20 April 2024

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Journal articles on the topic "Variables action-Angles"

1

Monari, G., B. Famaey, J. B. Fouvry, and J. Binney. "Distribution functions for resonantly trapped orbits in our Galaxy." Proceedings of the International Astronomical Union 13, S334 (2017): 341–42. http://dx.doi.org/10.1017/s1743921317006688.

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AbstractWe show how to capture the behaviour of the phase-space distribution function (DF) of a Galactic disc stellar population at a resonance. This is done by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then assign to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits only depends on the new se

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2

VIROVLYANSKY, A. L. "RAY CHAOS IN UNDERWATER ACOUSTIC WAVEGUIDES." International Journal of Bifurcation and Chaos 18, no. 09 (2008): 2693–700. http://dx.doi.org/10.1142/s0218127408021907.

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The chaotic motion of a ray path in a deep water acoustic waveguide with internal-wave-induced fluctuations of the sound speed is investigated. A statistical approach for the description of chaotic rays is discussed. The behavior of ray trajectories is studied using Hamiltonian formalism expressed in terms of action-angle variables. It is shown that the range dependence of the action variable of chaotic ray can be approximated by a random Wiener process. On the basis of this result, analytical expressions for probability density functions of ray parameters are derived. Distributions of coordin

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3

Zhu, W. Q., Z. L. Huang, and Y. Q. Yang. "Stochastic Averaging of Quasi-Integrable Hamiltonian Systems." Journal of Applied Mechanics 64, no. 4 (1997): 975–84. http://dx.doi.org/10.1115/1.2789009.

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A stochastic averaging method is proposed to predict approximately the response of quasi-integrable Hamiltonian systems, i.e., multi-degree-of-freedom integrable Hamiltonian systems subject to lightly linear and (or) nonlinear dampings and weakly external and (or) parametric excitations of Gaussian white noises. According to the present method an n-dimensional averaged Fokker-Planck-Kolmogrov (FPK) equation governing the transition probability density of n action variables or n independent integrals of motion can be constructed in nonresonant case. In a resonant case with α resonant relations,

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4

Famaey, B., G. Monari, A. Siebert, J. B. Fouvry, and J. Binney. "Distribution functions for Galactic disc stellar populations in the presence of non-axisymmetric perturbations." Proceedings of the International Astronomical Union 13, S334 (2017): 195–98. http://dx.doi.org/10.1017/s174392131700672x.

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AbstractThe present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential, in the form of a bar or spiral arms, can be treated, away from the main resonances, through perturbation theory within the action-angle coordinates of the unperturbed axisymmetric system. The first order moments of such a perturbed distribution function (DF) in the presence of spiral arms give rise to non-zero radial and vertical mean stellar velocities, called breathing modes. Such an Eulerian linearized treatment however diverges at resonances. The Lagrangian approach t

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5

KOBE, DONALD H. "INVARIANCE OF THE GENERALIZED HANNAY ANGLE UNDER GAUGE TRANSFORMATIONS: APPLICATION TO THE TIME-DEPENDENT GENERALIZED HARMONIC OSCILLATOR." International Journal of Modern Physics B 07, no. 11 (1993): 2147–62. http://dx.doi.org/10.1142/s021797929300281x.

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The Hannay angle of classical mechanics is generalized so that it is invariant under gauge transformations, which are a restricted class of canonical transformations. A distinction between the Hamiltonian and the energy is essential to make in time-dependent problems. A time-dependent generalized harmonic oscillator with a cross term in the Hamiltonian is taken as an example. The Hamiltonian of this system is not in general the energy. The energy, the time derivative of which is the power, is obtained from the equation of motion and related to the action variable. Hamilton’s equations give the

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6

McGibbon, Chris A., and David E. Krebs. "Discriminating age and disability effects in locomotion: neuromuscular adaptations in musculoskeletal pathology." Journal of Applied Physiology 96, no. 1 (2004): 149–60. http://dx.doi.org/10.1152/japplphysiol.00422.2003.

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We identified biomechanical variables indicative of lower extremity dysfunction, distinct from age-related gait adaptations, and examined interrelationships among these variables to better understand the neuromuscular adaptations in gait. Sagittal plane ankle, knee, and hip peak angles, moments, and powers and spatiotemporal parameters were acquired during preferred-speed gait in 120 subjects: 45 healthy young, 37 healthy elders, and 38 elders with functional limitations due to lower extremity musculoskeletal pathology, primarily arthritis. Multiple analysis of covariance with discriminate ana

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7

Zhu, W. Q., and Y. Q. Yang. "Exact Stationary Solutions of Stochastically Excited and Dissipated Integrable Hamiltonian Systems." Journal of Applied Mechanics 63, no. 2 (1996): 493–500. http://dx.doi.org/10.1115/1.2788895.

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It is shown that the structure and property of the exact stationary solution of a stochastically excited and dissipated n-degree-of-freedom Hamiltonian system depend upon the integrability and resonant property of the Hamiltonian system modified by the Wong-Zakai correct terms. For a stochastically excited and dissipated nonintegrable Hamiltonian system, the exact stationary solution is a functional of the Hamiltonian and has the property of equipartition of energy. For a stochastically excited and dissipated integrable Hamiltonian system, the exact stationary solution is a functional of n ind

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8

Dmitriev, Vladimir G., Alexander N. Danilin, Anastasiya R. Popova, and Natalia V. Pshenichnova. "Numerical Analysis of Deformation Characteristics of Elastic Inhomogeneous Rotational Shells at Arbitrary Displacements and Rotation Angles." Computation 10, no. 10 (2022): 184. http://dx.doi.org/10.3390/computation10100184.

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Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line. A finite difference method (FDM) is used to discretize the original continuum problem in spatial variables, replacing the differential operators with a second-order finite difference approximation. The computational algorithm for solving the nonlinear boundary value problem is based on a quasi-dynamic form of the ascertainment method with the const

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9

Fan, Zihao, Yang Xu, Yuhang Kang, and Delin Luo. "Air Combat Maneuver Decision Method Based on A3C Deep Reinforcement Learning." Machines 10, no. 11 (2022): 1033. http://dx.doi.org/10.3390/machines10111033.

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To solve the maneuvering decision problem in air combat of unmanned combat aircraft vehicles (UCAVs), in this paper, an autonomous maneuver decision method is proposed for a UCAV based on deep reinforcement learning. Firstly, the UCAV flight maneuver model and maneuver library of both opposing sides are established. Then, considering the different state transition effects of various actions when the pitch angles of the UCAVs are different, the 10 state variables including the pitch angle, are taken as the state space. Combined with the air combat situation threat assessment index model, a two-

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10

Hu, Zhizheng, Haifeng Zeng, Yun Ge, Wendong Wang, and Jiangkun Wang. "Simulation and Experiment of Gas-Solid Flow in a Safflower Sorting Device Based on the CFD-DEM Coupling Method." Processes 9, no. 7 (2021): 1239. http://dx.doi.org/10.3390/pr9071239.

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To study the movement characteristics and separation mechanism of safflower petals and their impurities under the action of airflow and lower the impurity rate in the cleaning operation process, integration of computational fluid dynamics (CFD) and discrete element method (DEM) codes was performed to study the motion and sorting behavior of impurity particles and safflower petals under different airflow inclination angles, dust removal angles and inlet airflow velocities by establishing a true particle model. In this model, the discrete particle phase was applied by the DEM software, and the c

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