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Necessary and sufficient conditions of existence of periodical motions in the model of a hinge mechanism in a flow

机译：流量中铰链机构模型中的期刊运动的必要条件

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Mathematical model of a one-degree-of-freedom hinge mechanism (wind power unit) interacting with a wind flow is introduced. Equations of motion of this device represent a second order system of autonomous ordinary differential equations. The common factor at terms corresponding to aerodynamic forces is assumed to be a small parameter. Thus, the system is close to a Hamiltonian one Both Hamiltonian and non-conservative parts of the system are essentially nonlinear. The Poincare-Pontryagin approach is used in order to obtain necessary and sufficient conditions of existence and orbital stability of periodic trajectories of the system. Attracting periodic trajectories correspond to operation modes of the wind power unit. Estimation of the trapped power for these regimes is obtained, and bifurcation diagrams of this power are constructed depending on parameters of the system.

机译：引入了与风流相互作用的一种自由度铰链机构（风电单元）的数学模型。该装置的运动方程代表了自主常微分方程的二阶系统。假设对应于空气动力力的术语的常见因素是一个小参数。因此，该系统接近Hamiltonian的一个汉密尔顿和系统的非保守部分基本上是非线性的。使用Poincare-pontryagin方法，以获得系统周期性轨迹的必要和充分的存在条件和轨道稳定性。吸引周期性轨迹对应于风电机的操作模式。获得了这些制度的捕获功率的估计，并且根据系统的参数构建该功率的分叉图。

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《International Conference on Structural Dynamics》|2017年|717-1434p.|共6页
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作者
Liubov Klimina; Boris Lokshin; Yury Selyutskiy;
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正文语种
中图分类结构动力学;
关键词
counter-rotating HAWT; closed dynamical model; operation modes; stability; parametric analysis; control.;

机译：反旋转Hawt;封闭的动态模型;操作模式;稳定性;参数分析;控制。;

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1. Necessary and sufficient conditions for existence of periodic motions of forced systems of particles [J] . Pedro J. Torres ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2001,第3期

机译：存在粒子强迫系统周期性运动的充要条件
2. Equivalent direct planning mechanisms in active systems sufficient conditions for their existence [J] . S. N. Petrakov Automation and Remote Control . 2001,第10期

机译：主动系统中的等效直接计划机制为其存在提供了充分条件
3. Sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control [J] . Chen FD, Lin FX, Chen XX Applied mathematics and computation . 2004,第1期

机译：一类具有反馈控制的中立时滞模型存在正周期解的充分条件
4. Necessary and sufficient conditions of existence of periodical motions in the model of a hinge mechanism in a flow [C] . Liubov Klimina, Boris Lokshin, Yury Selyutskiy International Conference on Structural Dynamics . 2017

机译：流量中铰链机构模型中的期刊运动的必要条件
5. Improved necessary and sufficient conditions for the existence of a subtle cardinal. [D] . Barendse, Peter. 2010

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6. Conditions Necessary and Sufficient for the Existence of a Stieltjes Integral [O] . R. D. Carmichael 1919

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Necessary and sufficient conditions of existence of periodical motions in the model of a hinge mechanism in a flow

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