一类滞后相对转动动力学方程的分岔特性及其解析近似解

建立了一类含Davidenkov滞后环的非线性相对转动动力学方程.分别分析了该非线性相对转动自治方程和微外扰下非自治方程的分岔特性，并采用KBM法求解了滞后环指数n=2时该非线性相对转动方程在周期激励下的解析近似解.通过数值仿真，得到了几种分岔结构及外扰下全局分岔图，同时将数值解与本文KBM法求解结果进行比较，证明本文求解结果有较高的精度，为研究这一类滞后相对转动系统提供了理论参考依据. 关键词： 相对转动 滞后环 分岔 KBM法     

相对转动动力学方程的稳定性及在一类黏弹性系数下的解

建立圆柱体任意两个截面间的一般黏弹性转动力学方程，讨论了相对转角的稳定性，由于此方程为变系数的二阶线性的非齐次常微分方程组，没有统一的求解方法.因此，针对其中的一类黏弹性系数求得其解. 关键词： 变系数方程的解 相对转角 稳定性     

相对转动非线性动力学方程的稳定性及在一类非线性弹性系数下的解

建立一类含非线性弹性力的二端面转轴相对转动非线性动力学方程.对相对转动非线性自治方程进行定性分析，研究方程的稳定性.用参数变换法求得相对转动非线性非自治方程在强迫激励下的高次近似解.     

二端面转轴相对转动非线性动力学系统的稳定性与近似解

建立了二端面转轴相对转动系统的非线性动力学方程.对于等力矩的动力学方程进行了定性分析，得到了方程的稳定性等性质.用平均方法求得方程在一定条件下的近似解. 关键词： 非线性动力学方程 稳定性 极限环 近似解     

相对转动非线性动力系统的稳定性与强迫激励下的近似解

研究相对转动非线性动力系统的运动稳定性.建立具有一般广义阻尼力和外扰激励的一类两质量相对转动非线性动力系统的动力学方程.研究相对转动非线性动力自治系统的稳定性，证明系统在一定条件下可发生闭轨分岔.应用多尺度法得到强迫激励下非自治系统的近似解. 关键词： 相对转动 非线性动力系统 运动稳定性 近似解     

一类非线性相对转动动力系统的平衡稳定性及组合谐波近似解

建立一类含广义非线性弹性力的两质量相对转动系统的非线性动力学方程. 应用变量梯度法构造李雅普诺夫函数，研究相对转动非线性自治系统的稳定性. 应用摄动法求得相对转动非线性非自治系统在两种不同频率谐波共同激励下的组合谐波响应的近似解. 关键词： 相对转动 非线性动力系统 稳定性 组合谐波响应     

用广义变分迭代理论求一类相对转动动力学方程的解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动扰动动力学方程. 首先利用变分原理构造了广义变分迭代, 其次决定方程的初始近似, 最后通过迭代表示式得到了对应方程的任意次近似解. 关键词： 相对转动 动力系统 变分迭代     

一类相对转动非线性动力学模型的近似解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动非线性动力学模型. 首先构造一个同伦映射, 其次决定方程的初始近似, 最后通过同伦映射方法得到了对应模型的任意次近似解. 关键词： 相对转动 非线性动力系统 近似解     

耦合相对转动非线性动力系统的稳定性与近似解

研究了一类含三次非线性耦合项的相对转动非线性动力系统的动力学行为. 建立了具有非线性弹性力、广义摩阻力耦合项的系统动力学方程. 运用多尺度法求解谐波激励下耦合非自治系统的近似解，通过讨论系统的主共振和内共振特性，分析了耦合项对系统响应的影响. 应用奇异性理论研究了主振稳态响应分岔方程的稳定性，得到了系统的转迁集和分岔曲线的拓扑结构. 关键词： 相对转动 非线性耦合动力系统 奇异性理论 稳定性     

一类谐波激励相对转动非线性动力系统的稳定性与近似解

建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析，通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解，同时分析了主振系统稳态运动的稳定性. 关键词： 相对转动 非线性动力系统 Lyapunov函数 稳定性     

Symmetric heat and mass transfer in a rotating spherical layer

The general theory of heat and mass transfer maintaining rotation with slightly different velocities under conditions typical for cores of planets in the solar system is developed for the first time. The analytic solution is obtained for thermal and diffusion equations without nonlinear terms responsible for the convective transfer. This spherically symmetric basic solution is applicable when the thermal flux from a planet core is weaker than or comparable to the adiabatic (radiative) flux. In the general case, by subtracting the basic solution, we simplified the inhomogeneous system of convective equations to obtain a completely homogeneous and dimensionless system. The latter system is controlled by two asymptotically small parameters: the Rossby number ε<10^?5, which characterizes the relative value of differential rotation, and the generalized Eckman number E<10^?12, which characterizes the relative role of viscosity-diffusion effects during rapid rotation. The principal order of the solution for ε →0 and then for \(\sqrt E \to 0\), for the transfer coefficients close to molecular coefficients, results in the basic flow, which is symmetric with respect to the rotation axis and directed predominantly along the azimuth. The basic-flow liquid ascends from a solid core along spirals inside an axial cylinder in contact with the equator of the solid core and descends in a narrow layer along the cylinder walls. The moment of viscous forces in the inner boundary Eckman layer provides a faster rotation of the inner solid core of terrestrial planets compared to a massive outer mantle due to the growth of the solid core at the expense of a low-density liquid core.     

Theory of ferromagnetic resonances in thin wires

A phenomenological theory of ferromagnetic resonances in a ferromagnetic metallic cylinder magnetized along its axis is based on the simultaneous solution of the equation of motion and Maxwell's equations. A general relaxation term in the equation of motion is used. The boundary conditions correspond to the dynamic surface anisotropy with the preferred direction parallel to the static magnetization. It is shown that the solution yields an infinite number of resonance modes of different spatial symmetry. Formulas for the surface impedance and the relative absorption of individual modes are derived. The effect of the finite radius of the cylinder on the resonance, antiresonance and spin wave resonance behaviour is discussed.     

一类非线性相对转动周期系统的平衡稳定性分析

利用一类周期性变系数线性常微分方程解的基本矩阵的Jordan形，分析一类非线性相对转动系统扭转的运动稳定性，从而得到非线性相对转动周期系统的运动稳定准则. 运用Lyapunov函数法，对广泛存在的一类机械传动系统的相对转动运动的平衡稳定位置的稳定域进行研究，并给出数学解析表达式. 这为工程中广泛存在的这类机械传动系统稳定工作区间工作参数的选取和相似模拟提供了理论依据及方法，据此可进一步分析和评价大型复杂旋转机械主传动系统的扭振稳定性. 关键词： 相对转动 相似模拟 运动稳定 平衡稳定     

具有一般非线性弹性力和广义阻尼力的相对转动非线性系统的周期解问题

讨论了一类相对转动非线性动力系统的周期解问题.首先建立了一类具有一般非线性弹性力、广义阻尼力和强迫周期力项的相对转动非线性动力系统;其次得到了对应自治系统的周期解不存在性结果,以及运用Mawhin重合度理论得到了该模型的周期解存在性结果,推广了已有的结果;最后举例证明本文结果的正确性.     

An elastodynamic solution of finite long orthotropic hollow cylinder under torsion impact

The paper presents an analytical method to solve the elastodynamic problem of a finite-length orthotropic hollow cylinder subjected to a torsion impact often occurring in engineering fields. The elastodynamic solution is composed of a quasi-static solution of homogeneous equation satisfied with the non-homogeneous boundary condition and a dynamic solution of non-homogeneous equation satisfied with homogeneous boundary condition. The quasi-static solution can be obtained by directly solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of a non-homogeneous dynamic equation is obtained by means of a finite Hankel transform to a radial variable r, Laplace transform to a time variable t and finite Fourier transform to an axial variable z. Thus, the elastodynamic solution of the finite length of an orthotropic hollow cylinder subjected to a torsion impact is obtained. On the other hand, a dynamic finite element for the same problem is also carried out by applying the ANSYS finite-element analysis system. Comparing the theoretical solution with finite-element solution, it can be found that two kinds of results obtained by making use of two different solving methods are suitably approached. Therefore, it is further concluded that the methods and computing processes of the theoretical solution are effective and accurate.     

Generalized radial oscillation modes of an acoustical medium rotating in a cylinder

Variants of closed wave equations for velocity perturbations in a rotating compressible medium (liquid or gas) are suggested. The effects of both the nonideal form of the equation of state of the medium and the character of its unperturbed state are taken into account in the equations. In the case of an ideal gas at an isothermal background state, these equations are solved exactly in analytic form, and the solutions describe the generalized radial oscillation modes. An inference is made about the existence of a shift of resonance frequencies of these modes because of the rotation of the medium. This shift is calculated as a function of the velocity of gas rotation and the radius of the cylinder.     

Rarefied molecular gas flow near the rotating cylindrical surface

An exact analytic solution of the problem of the right circular cylinder in a rarefied molecular gas is constructed in the isothermal approximation. An expression for the velocity of a rarefied molecular gas entrained by the cylinder rotated therein is obtained in the regime of a flow with slip accounting for the second-order correction in terms of the Knudsen number. A generalization of the BGK model of the Boltzmann kinetic equation accounting for the rotational degrees of freedom of gas molecules is used as the governing equation, and the diffuse reflection model is used as a microscopic boundary condition on the cylinder surface. The given approach is shown to enable the consideration of the gas flow dependence on the Prandtl number and the gas temperature.