A stabilization of constraints in the numerical solution of euler - lagrange equation 方程數(shù)值求解的一種違約穩(wěn)定性方法
A stabilization of constraints for the numerical solution of euler - lagrange equation in multi - body system 方程數(shù)值計(jì)算的一類違約修正法
Least square algorithms and constraint stabilization for euler - lagrange equations of multibody system dynamics 方程的最小二乘法與違約修正
In this paper , we convert the complex third order eigenvalue problems into the real third order eigenvalue problems . then , based on the euler - lagrange equation and legendre transformation , a reasonable jacobi - ostrogredsky coordinate system have been found , then using nonlinear method , the lax pairs of the real bargrnann and neumann system are nonlinearized , so as to be a new finite - dimensional integrable hamilton system in the liouville sense is generated . moreover , the involutive representations of the solution for the evolution equations are obtained 本文將復(fù)的三階特征值問題轉(zhuǎn)化為實(shí)的三階特征值問題,利用euler - lagrange方程和legendre變換,找到一組合理的實(shí)的jacobi - ostrogredsky坐標(biāo)系,從而找到與之相關(guān)的實(shí)化系統(tǒng),再利用曹策問教授的非線性化方法,分別將三階特征值問題及相應(yīng)的lax對(duì)進(jìn)行非線性化,從而得到bargmann勢(shì)和neumann勢(shì)約束系統(tǒng),并證明它們是liouville意義下的完全可積系統(tǒng),進(jìn)而給出了bargmann系統(tǒng)和neumann系統(tǒng)的對(duì)合解。
Only some fundamental parameters are posted to servers , which can complete the modeling , numerical analysis , management , and animation simulation . the results are given to the client . the distributed simulation system can automatically build myltibody systems dynamics equations using euler - lagrange equations in global coordinates 用戶可以在客戶端提交運(yùn)動(dòng)學(xué)仿真所需要的基本參數(shù),在服務(wù)器端完成系統(tǒng)數(shù)學(xué)模型的自動(dòng)建立、數(shù)值分析及數(shù)據(jù)管理,相應(yīng)的數(shù)據(jù)和圖形仿真結(jié)果反饋回客戶端。
For the regular curves , we find two killing fields for the purpose of integrating the structural equations of the p - elastic curves and express the p - elastica by quadratures in a system of cylindrical coordinates . for the star - like affine curves , we solve the euler - lagrange equation by quadratures and reduced the higher order structure equation to a first order linear system by using killing field and the classification of linear lie algebra sl ( 2 , r ) , sl ( 3 , r ) and sl ( 4 , r ) . we solve the centroaffine p - elastica completely by quadratures 對(duì)于正則曲線的情形,我們發(fā)現(xiàn)了兩個(gè)用于求解p -彈性曲線的結(jié)構(gòu)方程的killing向量場(chǎng)并用積分將p -彈性曲線在一個(gè)柱面坐標(biāo)系中表示出來,而對(duì)仿射星形曲線的情形,我們用積分方法解出了歐拉-拉格朗日方程,利用killing向量場(chǎng)及線性李代數(shù)s1 ( 2 , r ) 、 s1 ( 3 , r )和s1 ( 4 , r )的分類將高階結(jié)構(gòu)方程降為一階線性方程,因此我們用積分完全解出了中心仿射p -彈性曲線。