本文選題：開普勒定律 + 軌道運動　； 參考：《中國科學:物理學 力學 天文學》2014年01期

【摘要】：本文運用Udwadia-Kalaba理論對天體運動進行了研究(尤其針對開普勒定律和萬有引力定律).我們用一種創(chuàng)新的方法表明天體的運行軌道可能是圓,橢圓,雙曲線或拋物線.并且,在UdwadiaKalaba理論基礎上,運用運行軌道約束(橢圓,圓環(huán),雙曲線或拋物線)以及角動量守恒約束核實了任何天體運動都遵從萬有引力定律.基于Udwadia-Kalaba理論,我們首先考慮無約束離散動態(tài)系統(tǒng),其運動方程可應用牛頓力學或拉格朗日力學以廣義坐標形式寫出.然后推導各類約束的二階約束方程.最后將額外的廣義力約束(從二階約束方程獲得)施加到無約束系統(tǒng)上.對多體系統(tǒng)使用此建模方法,我們總能推導出Udwadia-Kalaba方程的顯式解析形式.Udwadia-Kalaba方程可用于解決完整或非完整約束問題以及理想或非理想約束問題.如果質量矩陣奇異,Udwadia-Kalaba方程也適用.
[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.
【作者單位】： 合肥工業(yè)大學 機械與汽車工程學院;Woodruff
【基金】：國家高技術研究發(fā)展計劃資助項目(編號:2012AA111711)
【分類號】：P13

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