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Academic literature on the topic 'Variables action-Angles'
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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 set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of distribution functions in action space.
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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 coordinates, momenta (grazing angles), and actions of sound rays are evaluated. Numerical simulation shows that statistical characteristics of ray parameters weakly depend on a particular realization of random perturbation giving rise to ray chaos.
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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, an (n + α)-dimensional averaged FPK equation governing the transition probability density of n action variables and α combinations of phase angles can be obtained. The procedures for obtaining the stationary solutions of the averaged FPK equations for both resonant and nonresonant cases are presented. It is pointed out that the Stratonovich stochastic averaging and the stochastic averaging of energy envelope are two special cases of the present stochastic averaging. Two examples are given to illustrate the application and validity of the proposed method.
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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 to the impact of non-axisymmetries at resonances avoids this problem. It is based on the construction of new orbital tori in the resonant trapping region, which come complete with a new system of angle-action variables. These new tori can be populated by phase-averaging the unperturbed DF over the new tori. 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 set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data with an action-based DF.
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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 time rate of change of the angle and action variables. The generalized Hannay angle is shown to be zero, and remains invariant under gauge transformations. On the other hand, if the original Hamiltonian is chosen as the energy, a nonzero generalized Hannay angle is obtained, but the power is given incorrectly. Nevertheless in the adiabatic limit, the total angle, which is the sum of the dynamical and Hannay angles, is equal to the one calculated from the correct energy.
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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 analysis, adjusted for gait speed, was used to identify the variables discriminating groups. Correlation analysis was used to explore interrelationships among these variables within each group. Healthy elders were discriminated (sensitivity 76%, specificity 82%) from young adults via decreased late-stance ankle plantar flexion angle, increased late-stance knee power absorption, and early-stance hip extensor power generation. Disabled elders were discriminated (sensitivity 74%, specificity 73%) from healthy elders via decreased late-stance ankle plantar flexor moment and power generation, increased early-stance ankle dorsiflexor moment, and late-stance hip flexor moment and power absorption. Relationships among variables showed a higher degree of coupling for the disabled elders compared with the healthy groups, suggesting a reduced ability to alter motor strategies. Our data suggest that, beyond age-related changes, elders with lower extremity dysfunction rely excessively on passive action of hip flexors to provide propulsion in late stance and contralateral ankle dorsiflexors to enhance stability. These findings support a growing body of evidence that gait changes with age and disablement have a neuromuscular basis, which may be informative in a motor control framework for physical therapy interventions.
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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 independent integrals of motion or n action variables of the modified Hamiltonian system in nonresonant case, or a functional of both n action variables and α combinations of phase angles in resonant case with α (1 ≤ α ⩽ n – 1) resonant relations, and has the property that the partition of the energy among n degrees-of-freedom can be adjusted by the magnitudes and distributions of dampings and stochastic excitations. All the exact stationary solutions obtained to date for nonlinear stochastic systems are those for stochastically excited and dissipated nonintegrable Hamiltonian systems, which are further generalized to account for the modification of the Hamiltonian by Wong-Zakai correct terms. Procedures to obtain the exact stationary solutions of stochastically excited and dissipated integrable Hamiltonian systems in both resonant and nonresonant cases are proposed and the conditions for such solutions to exist are deduced. The above procedures and results are further extended to a more general class of systems, which include the stochastically excited and dissipated Hamiltonian systems as special cases. Examples are given to illustrate the applications of the procedures.
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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 construction of an explicit two-layer time-difference scheme of second-order accuracy. The influence of physical and mechanical characteristics of isotropic and composite materials on the deformation features of elastic spherical shells under the action of surface loading of “tracking” type is investigated. The results of the studies conducted have shown that the physical and mechanical characteristics of isotropic and composite materials significantly affect the nature of the deformation of the clamped spherical shell in both the subcritical and post-critical domains. The developed mathematical models and computational algorithms can be applied in the future to study shells of rotation made of hyperelastic (non-linearly elastic) materials and soft shells.
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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-layer reward mechanism combining internal reward and sparse reward is designed as the evaluation basis of reinforcement learning. Then, the neural network model of the full connection layer is built according to an Asynchronous Advantage Actor–Critic (A3C) algorithm. In the way of multi-threading, our UCAV keeps interactively learning with the environment to train the model and gradually learns the optimal air combat maneuver countermeasure strategy, and guides our UCAV to conduct action selection. The algorithm reduces the correlation between samples through multi-threading asynchronous learning. Finally, the effectiveness and feasibility of the method are verified in three different air combat scenarios.
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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 continuum gas phase was described by the ANSYS Fluent software. The Box-Behnken experimental design with three factors and three levels was performed, and parameters such as inlet airflow velocity, airflow inclined angle, and dust remover angle were selected as independent variables that would influence the cleaning impurity rate and the cleaning loss rate. A mathematical model was established, and then the effects of various parameters and their interactions were analyzed. The test results show that the cleaning effect is best when the inlet airflow velocity is 7 m/s, the airflow inclined angle is 0°, and the dust remover angle is 25°. Confirmatory tests showed that the average cleaning impurity rate and cleaning loss rate were 0.69% and 2.75%, respectively, which dropped significantly compared with those from previous optimization. An experimental device was designed and set up; the experimental results were consistent with the simulation results, indicating that studying the physical behavior of safflower petals-impurity separation in the airflow field by using the DEM-CFD coupling method is reliable. This result provides a basis for follow-up studies of separation and cleaning devices for lightweight materials such as safflower petals.