| 扭称运动方程的线性近似解析解 |
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| 引用本文： | 范淑华,罗俊,李建国.扭称运动方程的线性近似解析解[J].华中科技大学学报(自然科学版),1993(6). |
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| 作者姓名： | 范淑华 罗俊 李建国 |
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| 作者单位： | 华中理工大学物理系
(范淑华)，华中理工大学引力实验中心
(罗俊)，华中理工大学引力实验中心(李建国) |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 给出了扭称受迫共振时,其振幅和位相的线性近似解析表达式.与理想情况(零级近似)相比,采用新表达式计算引力常数G,相对修正达10~(-3)量级.
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| 关 键 词： | 扭称振幅 线性近似 引力常数 机械共振 |
The Analytical Solution of the Motional Equation of Torsion Balance in Linear Approximation |
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| Fan Shuhua Luo Jun Li Jianguo.The Analytical Solution of the Motional Equation of Torsion Balance in Linear Approximation[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,1993(6). |
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| Authors: | Fan Shuhua Luo Jun Li Jianguo |
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| Institution: | Fan Shuhua Luo Jun Li Jianguo |
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| Abstract: | In the experiment on measuring the gravitational constant G with a mechanical resonance method,the distance between the centers of the attracting mass and test mass is a variable. The gravitational torque acting on the torsion balance (or test body) is not a simple sinusoidal function. The motion of torsion balance should be described by a nonlinear differential equation. In this paper,the authors have derived the exact expression for the gravitational torque. By assuming a linear approximation on the amplitude of torsion balance,the analytical solution of the motional equation has been obtained. The result of numerical estimation shows that relative correction can reach the orders of 10-3 with the new formula for determining the gravitational constant G. |
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| Keywords: | amplitude of torsion balance linear approximation gravitational constant mechanical resonance |
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