【摘要】：對(duì)于完整力學(xué)系統(tǒng),若選取的參數(shù)不是完全獨(dú)立的,則稱為有多余坐標(biāo)的完整系統(tǒng).由于完整力學(xué)系統(tǒng)的第二類Lagrange方程中沒有約束力,故為研究完整力學(xué)系統(tǒng)的約束力,需采用有多余坐標(biāo)的帶乘子的Lagrange方程或第一類Lagrange方程.一些動(dòng)力學(xué)問題要求約束力不能為零,而另一些問題要求約束力很小.如果約束力為零,則稱為系統(tǒng)的自由運(yùn)動(dòng)問題.本文提出并研究了有多余坐標(biāo)完整系統(tǒng)的自由運(yùn)動(dòng)問題.為研究系統(tǒng)的自由運(yùn)動(dòng),首先,由d’Alembert--Lagrange原理,利用Lagrange乘子法建立有多余坐標(biāo)完整系統(tǒng)的運(yùn)動(dòng)微分方程;其次,由多余坐標(biāo)完整系統(tǒng)的運(yùn)動(dòng)方程和約束方程建立乘子滿足的代數(shù)方程并得到約束力的表達(dá)式;最后,由約束系統(tǒng)自由運(yùn)動(dòng)的定義,令所有乘子為零,得到系統(tǒng)實(shí)現(xiàn)自由運(yùn)動(dòng)的條件.這些條件的個(gè)數(shù)等于約束方程的個(gè)數(shù),它們依賴于系統(tǒng)的動(dòng)能、廣義力和約束方程,給出其中任意兩個(gè)條件,均可以得到實(shí)現(xiàn)自由運(yùn)動(dòng)時(shí)對(duì)另一個(gè)條件的限制.即當(dāng)給定動(dòng)能和約束方程,這些條件會(huì)給出實(shí)現(xiàn)自由運(yùn)動(dòng)時(shí)廣義力之間的關(guān)系.當(dāng)給定動(dòng)能和廣義力,這些條件會(huì)給出實(shí)現(xiàn)自由運(yùn)動(dòng)時(shí)對(duì)約束方程的限制.當(dāng)給定廣義力和約束方程,這些條件會(huì)給出實(shí)現(xiàn)自由運(yùn)動(dòng)時(shí)對(duì)動(dòng)能的限制.文末,舉例并說明方法和結(jié)果的應(yīng)用.
[Abstract]:For holonomic mechanical systems, if the selected parameters are not completely independent, they are called holonomic systems with redundant coordinates. Because there is no binding force in the Lagrange equation of the second kind of holonomic mechanical system, in order to study the binding force of holonomic mechanical system, the Lagrange equation with superfluous coordinates or the Lagrange equation of the first kind should be adopted. Some dynamic problems require no binding force, while others require little binding force. If the binding force is zero, it is called the free motion of the system. In this paper, the problem of free motion of a system with redundant coordinate holonomic system is proposed and studied. In order to study the free motion of the system, the differential equations of motion of the system with redundant coordinates are established by using the d'Alembert--Lagrange principle and the Lagrange multiplier method. Secondly, the algebraic equations satisfied by the multipliers are established by the equations of motion and constraint equations of the holonomic system with redundant coordinates and the binding expressions are obtained. Finally, by the definition of free motion of constrained system, all multipliers are zero, and the condition of realizing free motion of system is obtained. The number of these conditions is equal to the number of constraint equations. They depend on the kinetic energy, generalized forces and constraint equations of the system. That is, given kinetic energy and constraint equation, these conditions will give the relationship between generalized forces when realizing free motion. Given the kinetic energy and the generalized force, these conditions will give the constraints on the constraint equation when the free motion is realized. Given the generalized force and the constraint equation, these conditions will give the restriction of kinetic energy when the free motion is realized. At the end of the paper, examples are given to illustrate the application of the method and the results.
【作者單位】： 北京理工大學(xué)宇航學(xué)院;北京理工大學(xué)數(shù)學(xué)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(10932002,11272050,11572034)
【分類號(hào)】：O316

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 龍運(yùn)佳;非完整系統(tǒng)的動(dòng)力學(xué)偏加速度方程[J];中國(guó)農(nóng)業(yè)大學(xué)學(xué)報(bào);1998年04期

2 方建會(huì);二階非Четаев型非完整系統(tǒng)的守恒律[J];應(yīng)用數(shù)學(xué)和力學(xué);2000年07期

3 喬永芬,馬云鵬;廣義完整系統(tǒng)的能量方程[J];黃淮學(xué)刊(自然科學(xué)版);1998年S3期

4 梅鳳翔,許學(xué)軍;廣義Chaplygin系統(tǒng)的約化[J];物理學(xué)報(bào);2005年09期

5 張秀梅;m階非完整系統(tǒng)的第一積分與積分不變量[J];遼寧工學(xué)院學(xué)報(bào);2000年06期

6 張相武;;高階非完整系統(tǒng)的高階廣義Appell方程[J];江西師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2006年02期

7 張秀梅;m階非完整系統(tǒng)的Appell型方程[J];錦州師范學(xué)院學(xué)報(bào)(自然科學(xué)版);1999年02期

8 李元成;高階單面非完整系統(tǒng)的Noether定理[J];長(zhǎng)沙大學(xué)學(xué)報(bào);2002年04期

9 李元成;二階單面非完整系統(tǒng)的Noether定理[J];廣西大學(xué)學(xué)報(bào)(自然科學(xué)版);2000年01期

10 張偉偉;方建會(huì);張斌;;事件空間離散完整系統(tǒng)的Noether理論[J];動(dòng)力學(xué)與控制學(xué)報(bào);2012年02期

，

本文編號(hào)：2309658