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创建时空可变系多线矢物理学(85)将多线矢正则方程扩展为共轭对称形式
(接(84))
与[矢A(X,n)],[矢B(X,n)]相互共轭的多线矢可分别记为:[矢A*(X,n)],[矢B*(X,n)],当有:
[矢B(X,n)]= [矢A*(X,n)时间导数];[矢B*(X,n)]= [矢A(X,n)时间导数];
[矢A(X,n)]= [矢B*(X,n)时间导数];[矢A*(X,n)]= [矢B(X,n)时间导数];
则Lagrange, Hamilton函数L,H可分别扩展表达为:
L=[矢B* (X,n)]点乘[矢B(X,n)]+[矢A* (X,n)]点乘[矢A(X,n)];
L=[矢B* (X,n)]点乘[矢B(X,n)]-[矢A* (X,n)]点乘[矢A(X,n)];
运动方程分别扩展成为:
(偏L/偏A(X,n)(x))-(d/dt(X))(偏L/偏(W(A(X,n)(x))A(X,n)(x)时间导数))=0;
(偏L/偏A*(X,n)(x))-(d/dt(X))(偏L/偏(W(A*(X,n)(x))A*(X,n)(x)时间导数))=0;
(偏L/偏B(X,n)(x))-(d/dt(X))(偏L/偏(W(B(X,n)(x))B(X,n)(x)时间导数))=0;
(偏L/偏B*(X,n)(x))-(d/dt(X))(偏L/偏(W(B*(X,n)(x))AB*(X,n)(x)时间导数))=0;
(偏H/偏A(X,n)(x))-(d/dt(X))(偏H/偏(W(A(X,n)(x))A(X,n)(x)时间导数))=0;
(偏H/偏A*(X,n)(x))-(d/dt(X))(偏H/偏(W(A*(X,n)(x))A*(X,n)(x)时间导数))=0;
(偏H/偏B(X,n)(x))-(d/dt(X))(偏H/偏(W(B(X,n)(x))B(X,n)(x)时间导数))=0;
(偏H/偏B*(X,n)(x))-(d/dt(X))(偏H/偏(W(B*(X,n)(x))AB*(X,n)(x)时间导数))=0;
(未完待续)
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