本文選題：開(kāi)普勒定律 + 軌道運(yùn)動(dòng)��； 參考：《中國(guó)科學(xué):物理學(xué) 力學(xué) 天文學(xué)》2014年01期

【摘要】：本文運(yùn)用Udwadia-Kalaba理論對(duì)天體運(yùn)動(dòng)進(jìn)行了研究(尤其針對(duì)開(kāi)普勒定律和萬(wàn)有引力定律).我們用一種創(chuàng)新的方法表明天體的運(yùn)行軌道可能是圓,橢圓,雙曲線或拋物線.并且,在UdwadiaKalaba理論基礎(chǔ)上,運(yùn)用運(yùn)行軌道約束(橢圓,圓環(huán),雙曲線或拋物線)以及角動(dòng)量守恒約束核實(shí)了任何天體運(yùn)動(dòng)都遵從萬(wàn)有引力定律.基于Udwadia-Kalaba理論,我們首先考慮無(wú)約束離散動(dòng)態(tài)系統(tǒng),其運(yùn)動(dòng)方程可應(yīng)用牛頓力學(xué)或拉格朗日力學(xué)以廣義坐標(biāo)形式寫(xiě)出.然后推導(dǎo)各類(lèi)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(wú)約束系統(tǒng)上.對(duì)多體系統(tǒng)使用此建模方法,我們總能推導(dǎo)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(wèn)題以及理想或非理想約束問(wèn)題.如果質(zhì)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(xué) 機(jī)械與汽車(chē)工程學(xué)院;Woodruff
【基金】：國(guó)家高技術(shù)研究發(fā)展計(jì)劃資助項(xiàng)目(編號(hào):2012AA111711)
【分類(lèi)號(hào)】：P13

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本文編號(hào)：1818709