搜索
x2.3|Lagranget=t0(a;b;c)~r=~r(a;b;c;t);xi=xi(a;b;c;t)a;b;ct\t=t0\(a;b;c)\(a;b;c)~V=@~r@t~a=@~V@t=@2~r@t2f(a;b;c;t)Euler~r=(x;y;z)~V=~V(~r;t)tM(x;y;z)±tN(x+±x;y+±y;z+±z)1~a=d~Vdt~a=@~V@t=lim±t!0~V(~r+±~r;t+±t)¡~V(~r;t)±t=lim±t!01±tÃ@~V@t±t+@~V@x±x+@~V@y±y+@~V@z±z!=lim±t!01±tÃ@~V@t±t+±~r¢r~V!=@~V@t+(~V¢r)~V=+f=f(~r;t)=f(x;y;z;t)dfdt=lim±t!0f(~r+±~r;t+±t)¡f(~r;t)±t=@f@t+(~V¢r)fddt=@@t+~V¢rddt=@@t+V1H1@@x1+V2H2@@x2+V3H3@@x3d½dt=0r½=08:d½dt=@½@t+(~V¢r)½=0@½@t=0)½=1~r=~r(a;b;c;t))~V(~r;t)~V=@~r@t=~V(a;b;c;t)(1)t~r(x;y;z)(a;b;c)xi=xi(a;b;c;t))8:a=a(~r;t)=a(x;y;z;t)b=b(~r;t)=b(x;y;z;t)c=c(~r;t)=c(x;y;z;t)(2)2a;b;c(2)(1)~V=~V(a(~r;t);b(~r;t);c(~r;t);t)=~V(~r;t)2~V(~r;t))~r=~r(a;b;c;t)~r(a;b;c)t~r=(x;y;z),~r=~r(a;b;c;t))t~r=(x;y;z)~V(~r;t)=d~rdt8:dxdt=Vx(x;y;z;t)dydt=Vy(x;y;z;t)dzdt=Vx(x;y;z;t)~V(~r;t)~r=~r(c1;c2;c3;t)(3)t=t0~r(t0)=(a;b;c)c1;c2;c3c1=c1(a;b;c);c2=c2(a;b;c);c3=c3(a;b;c)(4)(4)(3))~r=~r(a;b;c;t)x2.4|1~r=~r(a;b;c;t)2d~rdt=~V(~r;t)8:dxdt=u(x;y;z;t)dydt=v(x;y;z;t)dzdt=w(x;y;z;t))8:x=x(c1;c2;c3;t)y=y(c1;c2;c3;t)z=z(c1;c2;c3;t)dxu(x;y;z;t)=dyv(x;y;z;t)=dzw(x;y;z;t)=dt3tx;y;zttd~r£~V=0)dxu(x;y;z;t)=dyv(x;y;z;t)=dzw(x;y;z;t)H1dq1V1(x;y;z;t)=H2dq2V2(x;y;z;t)=H3dq3V3(x;y;z;t)tu=y+Acost;v=1¡x;w=01dxdt=u=y+Acost(5)dydt=v=1¡x(6)dzdt=w=0(7)(6)d2ydt2=¡dxdt=¡y¡Acostd2ydt2+y=¡Acost4y=c1sint+c2cost¡A2tsint(6)x=1¡c1cost+(c2+A2)sint+A2tcost(7)z=c3t=0(x;y;z)=(x0;y0;z0)c1=1¡x0;c2=y0;c3=z08:x=1¡(1¡x0)cost+(y0+A2)sint+A2tcosty=(1¡x0)sint+y0cost¡A2tsintz=z02dxu=dyv=dzw=)dxy+Acost=dy1¡x=dz0)dz=0;z=c1(1¡x)dx=(y+Acost)dy2x¡x2=y2+2Aycost¡c1((x¡1)2+(y+Acost)2=A2cos2t+c1+1z=c2(x1;y1;z1)((x¡1)2+(y+2Acost)2=(x1¡1)2+(y1+2Acost)2z=z1a~n~V¢~n=0F(x;y;z)=0~V¢rF=0bc5(a;b;c)~r=(x;y;z)=(aet¡t¡1;be¡t+t¡1;c)(a;b;c)=³(x+t+1)e¡t;(y¡t+1)et;z´~r8:u=dxdt=aet¡1v=dydt=¡be¡t+1w=0a;b;c~V=(u;v;w)=(x+t;t¡y;0)1(a;b;c)a;b;c2dxx+t=dyt¡y=dz0((x+t)(y¡t)=c1z=c26