A stabilization of constraints in the numerical solution of euler - lagrange equation 方程數值求解的一種違約穩定性方法
A stabilization of constraints for the numerical solution of euler - lagrange equation in multi - body system 方程數值計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 本文將復的三階特征值問題轉化為實的三階特征值問題,利用euler - lagrange方程和legendre變換,找到一組合理的實的jacobi - ostrogredsky坐標系,從而找到與之相關的實化系統,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的lax對進行非線性化,從而得到bargmann勢和neumann勢約束系統,并證明它們是liouville意義下的完全可積系統,進而給出了bargmann系統和neumann系統的對合解。
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動學仿真所需要的基本參數,在服務器端完成系統數學模型的自動建立、數值分析及數據管理,相應的數據和圖形仿真結果反饋回客戶端。
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 對于正則曲線的情形,我們發現了兩個用于求解p -彈性曲線的結構方程的killing向量場并用積分將p -彈性曲線在一個柱面坐標系中表示出來,而對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向量場及線性李代數s1 ( 2 , r ) 、 s1 ( 3 , r )和s1 ( 4 , r )的分類將高階結構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。