扭转陀螺的运动研究

运用欧拉动力学方程分析了扭转陀螺的力学特性,从理论上预测了陀螺释放后250s内的运动情况,实验研究了陀螺的定轴性和进动性对陀螺运动的影响.实验结果表明:在初始扭转力矩变大时,进动角与章动角的角速度与角度峰值都会变大,但变化周期几乎不变.     

基于解析结果的拉格朗日陀螺运动特性分析

本文建立拉格朗日陀螺运动方程的解析方法.导出拉格朗日陀螺做规则进动的条件,用级数展开技术得到规则进动附近的小角度章动和进动的解析解.给出陀螺自转轴运动的简明图像,即重力引起绕竖直轴的规则进动和无重力的自由进动的叠加.利用解析结果对陀螺不倒之谜给出解释.     

环电流磁矩进动的演示与分析

给出一种可有效地演示电子轨道磁矩在外磁场中的进动规律的环电流陀螺,以及演示涡流存在的导体陀螺,并给出了相应分析．     

陀螺进动特性的研究

本文基于陀螺进动原理,推导出陀螺进动时的角速度和自转角速度关系式,结合电磁感应原理和光敏电阻特性制作了陀螺实验装置,同时精确测出陀螺的公转周期与自转周期,进一步计算了陀螺的转动惯量,并用平行轴定理所得的计算结果验证了此装置的理论方法与测量结果的正确性.     

扭转陀螺运动系统的研究

研究了扭转陀螺系统的角动量以及系统所受外力矩,分析了陀螺在运动中出现的进动、章动等现象.当陀螺存在一定偏心差时,陀螺会进行参变共振、受迫共振.     

广义相对论和Brans-Dicke引力理论下的行星进动与星光偏折

作为两种重要的候选引力理论,广义相对论以及Brans-Dicke引力理论对于理解天体及宇宙的形成与演化具有重要的意义.本文在广义相对论和Brans-Dicke引力理论下,考察恒星附近的行星进动以及星光偏折效应.首先推导出恒星周围的静态球对称背景时空下粒子轨道方程的普适形式;然后分别针对两种引力理论,进一步利用相应的真空场方程的静态球对称精确解推导出描述行星及星光轨道方程,其为非线性的二阶常微分方程;利用微扰法求解轨道方程,得到了含高阶修正的近似解,进而给出了对应的行星进动角和星光偏折角.本文对利用更高精度的实验观测来检验、甄别引力理论具有重要的意义.     

测定陀螺进动角速度的实验方法

陀螺是一种回转仪，它能显示出回转效应.回转仪的回转效应在科学上和技术上有广泛应用，例如，炮膛内部刻有螺旋式来复线，使射出的炮弹绕几何轴作高速旋转，成为回转仪等等.在微观世界中，具有自旋的电子、原子核和其他基本粒子放在磁场中，受到磁场的力矩也将和陀螺一样，产生进动.这一切都说明进动的重要，对进动角速度的测量，能进一步加深对进动的理解.一、测量原理陀螺可以以很高的转速绕它的自转轴旋转.当它的自转轴和铅直方向偏离时，陀螺受它本身的重力矩的作用，其自转轴绕铅直轴进动而不倒下，这就是陀螺的回转效应.图1是一精制…     

用时空线分析多普勒效应

采用描述波源运动，观察者运动及声波在静止空气中以声速传播的三组时空线，用几何方法导出多普勒公式，并通过时空线相交分析多普勒效应中观察者接收声波信号的时序及周期，着重讨论了一般文献中未曾涉及的不同条件下多普勒效应的结果及其物理意义。     

陀螺进动中的“角动量不守恒”问题

一些力学教科书中对回转效应的讲解就是直接利用重力力矩导致陀螺角动量变化得到均匀进动角速度,但是这会导致竖直方向出现进动角动量而无法解释的问题,即看似角动量不守恒。本文从基本的力学原理出发,分析了陀螺水平释放后从开始到稳定过程中的进动和章动,并对结果进行了数值模拟,证明忽略进动阻尼时稳定进动角动量与陀螺下倾导致的自转角动量竖直分量大小相等、方向相反,保证了系统竖直方向角动量恒为零。     

非对易时空下Gibbons-Maeda dilaton黑洞和Garfinkle-Horowitz-Strominger dilaton黑洞的热力学性质

以Gibbons-Maeda dilaton黑洞和Garfinkle-Horowitz-Strominger dilaton黑洞为例，研究空间的非对易性对黑洞热力学性质的影响.通过对比对易时空中Gibbons-Maeda dilaton黑洞和非对易时空中Garfinkle-Horowitz-Strominger dilaton黑洞的温度，得出如下结论：从对黑洞热力学性质产生影响这一角度来说，时空的非对易性和黑洞的荷(电荷或磁荷)有相似的作用.     

Gyroscopic Precession and Centrifugal Force in the Ernst Spacetime

The phenomenon of gyroscopic precession in the Ernst spacetime is studied within the framework of the Frenet-Serret formalism. General formulae are obtained for circular orbits. At the same time general relativistic analogues of inertial forces such as gravitational and centrifugal forces are also investigated in the Ernst spacetime. Reversal of gyroscopic precession as well as centrifugal force is considered at the circular photon orbits. These phenomena are examined in the Melvin universe as a special case of the Ernst spacetime by setting the mass parameter equal to zero.     

Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gravi-electric and gravi-magnetic fields are studied and their relation to inertial forces is established.     

A tapered beam finite element for rotor dynamics analysis

The stiffness, mass and gyroscopic matrices of a rotating beam element are developed, a cubic function being used for the transverse displacement. Shear deflection is included by use of end nodal variables of shear strain, along with transverse displacement and cross-section rotation; rotatory inertia effects are included in the energy functional to provide a Timoshenko beam formulation. The gyroscopic effects for small perturbations are linearized as a skew symmetric damping matrix. The formulation is implemented by numerical integration for a linearly tapered circular beam. A technique of reduction of the shear nodal variable prior to global assembly is shown to provide little loss in accuracy with reduced system bandwidth. Numerical comparisons for three previously published beam models are included, with results presented for the case of forward and reverse precession to verify the gyroscopic effects. The utility of the element in a general program for rotor dynamics analysis is identified.     

Coupled dilaton and electromagnetic field in cylindrically symmetric spacetime

An exact solution is obtained for coupled dilaton and electromagnetic field in a cylindrically symmetric spacetime where an axial magnetic field as well as a radial electric field both are present. Depending on the choice of the arbitrary constants our solution reduces either to dilatonic gravity with pure electric field or to that with pure magnetic field. In the first case we have a curvature singularity at a finite distance from the axis indicating the existence of the boundary of a charged cylinder which may represent the source of the electric field. For the second case we have a singularity on the axis. When the dilaton field is absent the electromagnetic field disappears in both the cases. Whereas the contrary is not true. It is further shown that light rays except for those proceeding in the radial direction are either trapped or escape to infinity depending on the magnitudes of certain constant parameters as well as on the nature of the electromagnetic field. Nature of circular geodesics is also studied in the presence of dilaton field in the cylindrically symmetric spacetime.     

Cosmological black holes: A black hole in the Einstein-de Sitter universe

As an example of a dynamical cosmological black hole, a spacetime that describes an expanding black hole in the asymptotic background of the Einstein-de Sitter universe is constructed. The black hole is primordial in the sense that it forms ab initio with the big bang singularity and its expanding event horizon is represented by a conformal Killing horizon. The metric representing the black hole spacetime is obtained by applying a time dependent conformal transformation on the Schwarzschild metric, such that the result is an exact solution with a matter content described by a two-fluid source. Physical quantities such as the surface gravity and other effects like perihelion precession, light bending and circular orbits are studied in this spacetime and compared to their counterparts in the gravitational field of the isolated Schwarzschild black hole. No changes in the structure of null geodesics are recorded, but significant differences are obtained for timelike geodesics, particularly an increase in the perihelion precession and the non-existence of circular timelike orbits. The solution is expressed in the Newman-Penrose formalism.     

Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle–Horowitz–Strominger (GHS) dilaton spacetime and Gibbons–Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.     

Charged rotating dilaton black branes in AdS universe

We present the metric for the (n + 1)-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.     

Polarized Spacetime Foam

An approximate model of a spacetime foam is presented. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. If we neglect of linear sizes of the quantum handle then it can be described with an operator containing a Grassman number and either a scalar or a spinor field. For both fields the Lagrangian is presented. For the scalar field it is the dilaton gravity + electrodynamics and the dilaton field is a dielectric permeability. The spherically symmetric solution in this case give us the screening of a bare electric charge surrounded by a polarized spacetime foam and the energy of the electric field becomes finite one. In the case of the spinor field the spherically symmetric solution give us a ball of the polarized spacetime foam filled with the confined electric field. It is shown that the full energy of the electric field in the ball can be very big.     

Conformal invariance of σ-models and classical string physics

We show that the identification of the conformal anomaly of the general bosonic two-dimensional non-linear σ-model as the generating functional for on-shell string scattering amplitudes is correct up toO(α′) terms. The absence, in the loop corrections to the spacetime effective action, of contributions from the explicit coupling to the dilaton field is suggested as a general feature for σ-models describing tree-level string physics.