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一切物体的基本特性和运动规律 (17)

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  • 2019-08-31 14:39:30

一切物体的基本特性和运动规律 (17)

((16))

44.各维速度矢量=各维距离矢量的时间导数,各维动量矢量=相应的质量乘各维速度矢量,各维力矢量=各维矢量的时间导数

   3维空间速度矢量:

v(3)[1线矢]={vj[j基矢],j=13求和}

=dr(3)[1线矢]/dt={drj[j基矢]/dt,j=13求和}

v(3)={vj^2,j=13求和}^(1/2)

=dr(3)/dt={(drj/dt)^2,j=13求和}^(1/2)

   3维空间动量矢量:

p(3)[1线矢]=mdr(3)[1线矢]/dt=m{drj[j基矢]/dt,j=13求和}

   4维时空速度矢量:

v(4)[1线矢]={va[a基矢],a=03求和}

=dr(4)[1线矢]/dt={dra[a基矢]/dt,a=03求和}

r0=ict,()r0=ia*t,()

  3维空间力矢量:

f(3)[1线矢]={fj[j基矢],j=13求和}

=dp(3)[1线矢]/dt={dpj[j基矢]/dt,j=13求和}

   4维时空速度矢量:

v(4)[1线矢]= dr(4)[1线矢]/dt= {dra[a基矢]/dt,a=03求和}

v(4)={va^2,a=03求和}^(1/2)

=ic{1-(vj/c)^2,j=13求和}^(1/2), ()

=ia* {1-(vj/a*)^2,j=13求和}^(1/2), ()

   4维时空动量矢量:

p(4)[1线矢]=mdr(4)[1线矢]/dt=m{dra[a基矢]/dt,a=03求和}

p(4)=mdr(4) /dt=m{va^2,a=03求和}^(1/2)

=icm{1-(vj/c)^2,j=13求和}^(1/2), ()

=ia*m{1-(vj/a*)^2,j=13求和}^(1/2), ()

vj^2,j=13求和=0,令m=m0,有:

m=m0/{1-(vj/c)^2,j=13求和}^(1/2), ()

 =m0/{1-(vj/a*)^2,j=13求和}^(1/2), ()

4维时空力矢量:

f(4)[1线矢]= dp(4)[1线矢]/dt= {dpa[a基矢]/dt,a=03求和}

f(4)={fa^2,a=03求和}^(1/2)

=ic{1-(fj/c)^2,j=13求和}^(1/2), ()

=ia* {1-(fj/a*)^2,j=13求和}^(1/2), ()

6维时空速度矢量:

v(6)[2线矢]={v0j [0j基矢]+vkl [kl基矢],jkl=123循环求和}

v(6)={v0j^2+vkl^2,jkl=123循环求和}^(1/2)

=ic{ (v0j)^2- (vkl/c)^2,jkl=123循环求和}^(1/2), ()

=ia*{ (v0j)^2- (vkl/a*)^2,jkl=123循环求和}^(1/2), ()

   6维时空动量矢量:

p(6)=m{v0j^2+vkl^2,jkl=123循环求和}^(1/2)

=icm{ (v0j)^2-(vkl/c)^2,jkl=123循环求和}^(1/2), ()

=ia*m{ (v0j)^2- (vkl/a*)^2,jkl=123循环求和}^(1/2), ()

(vkl)^2,jkl=123循环求和=0

m{ (v0j)^2,j=13求和}^(1/2)=m0,有:

m==m0/{(v0j)^2,j=13求和}^(1/2)

6维时空力矢量:

f(6)[2线矢]={f0j [0j基矢]+fkl [kl基矢],jkl=123循环求和}

f(6)={f0j^2+fkl^2,jkl=123循环求和}^(1/2)

=ic{ (f0j)^2-(fkl/c)^2,jkl=123循环求和}^(1/2), ()

=ia*{ (f0j)^2- (fkl/a*)^2,jkl=123循环求和}^(1/2), ()

12维时空速度矢量:

v(12)[22,1线矢]= {vkl,lj,0 [kl,lj,0基矢] +vkl,jk,0 [kl,jk,0基矢]

+vkl,kl,0 [kl,kl,0基矢]+v0k,0l,jj [0k,0l,j基矢],jkl=123循环求和}

v(12)=ic{vkl,lj,0^2+vkl,jk,0 ^2+vkl,kl,0^2

   +(v0k,0l,jj/c)^2,jkl=123循环求和}^(1/2) ()

    ia*{vkl,lj,0^2 +vkl,jk,0 ^2+vkl,kl,0^2

   +(v0k,0l,jj/a*)^2,jkl=123循环求和}^(1/2) ()

   12维时空动量矢量:

p(6)==icm{vkl,lj,0^2 +vkl,jk,0 ^2+vkl,kl,0^2

   +(v0k,0l,jj/c)^2,jkl=123循环求和}()

    ia*m{vkl,lj,0^2 +vkl,jk,0 ^2+vkl,kl,0^2

   +(v0k,0l,jj/a*)^2,jkl=123循环求和}()

(v0k,0l,jj/a*)^2,jkl=123循环求和=0

m{(v0k,0l,jj/a*)^2,jkl=123循环求和}^(1/2)=m0,有:

m==m0/{(v0k,0l,jj/a*)^2,jkl=123循环求和}^(1/2)

12维时空力矢量:

f(12)[22,1线矢]= {fkl,lj,0 [kl,lj,0基矢] +fkl,jk,0 [kl,jk,0基矢]

+fkl,kl,0 [kl,kl,0基矢]+f0k,0l,jj [0k,0l,j基矢],jkl=123循环求和}

f(12)=ic{ffkl,lj,0^2+fkl,jk,0 ^2+fkl,kl,0^2

   +(f0k,0l,jj/c)^2,jkl=123循环求和}^(1/2) ()

    ia*{fkl,lj,0^2 +fkl,jk,0 ^2+fkl,kl,0^2

   +(f0k,0l,jj/a*)^2,jkl=123循环求和}^(1/2) ()

(未完待续)

本文在科学网链接地址:http://blog.sciencenet.cn/blog-226-1196035.html


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