应用Udwadia-Kalaba理论对开普勒定律的研究

发布时间：2018-04-29 06:07

本文选题：开普勒定律 + 轨道运动　；参考：《中国科学:物理学力学天文学》2014年01期

【摘要】：本文运用Udwadia-Kalaba理论对天体运动进行了研究(尤其针对开普勒定律和万有引力定律).我们用一种创新的方法表明天体的运行轨道可能是圆,椭圆,双曲线或抛物线.并且,在UdwadiaKalaba理论基础上,运用运行轨道约束(椭圆,圆环,双曲线或抛物线)以及角动量守恒约束核实了任何天体运动都遵从万有引力定律.基于Udwadia-Kalaba理论,我们首先考虑无约束离散动态系统,其运动方程可应用牛顿力学或拉格朗日力学以广义坐标形式写出.然后推导各类约束的二阶约束方程.最后将额外的广义力约束(从二阶约束方程获得)施加到无约束系统上.对多体系统使用此建模方法,我们总能推导出Udwadia-Kalaba方程的显式解析形式.Udwadia-Kalaba方程可用于解决完整或非完整约束问题以及理想或非理想约束问题.如果质量矩阵奇异,Udwadia-Kalaba方程也适用.
[Abstract]:In this paper, the motion of celestial bodies is studied by using Udwadia-Kalaba theory (especially for Kepler's law and universal gravitation law). We use an innovative method to show that the celestial body's orbit may be a circle, an ellipse, a hyperbolic or a parabola. On the basis of UdwadiaKalaba's theory, using orbit constraints (ellipse, ring, hyperbolic or parabola) and angular momentum conserved constraints, it is verified that any celestial body motion obeys the law of universal gravity. Based on the Udwadia-Kalaba theory, we first consider the unconstrained discrete dynamic system. The equations of motion can be written in the form of generalized coordinates by Newtonian mechanics or Lagrange mechanics. Then the second order constraint equations of all kinds of constraints are derived. Finally, additional generalized force constraints (obtained from second-order constraint equations) are applied to unconstrained systems. Using this modeling method for multibody systems, we can always derive the explicit analytic form of Udwadia-Kalaba equation. Udwadia-Kalaba equation can be used to solve holonomic or nonholonomic constraint problems and ideal or non-ideal constraint problems. The Udwadia-Kalaba equation is also applicable if the mass matrix is singular.
【作者单位】：合肥工业大学机械与汽车工程学院;Woodruff
【基金】：国家高技术研究发展计划资助项目(编号:2012AA111711)
【分类号】：P13

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