||
一切物体的基本特性和运动规律 (17)
(接(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=1到3求和}
=dr(3)[1线矢]/dt={drj[j基矢]/dt,j=1到3求和},
v(3) ={vj^2,j=1到3求和}^(1/2)
=dr(3) /dt={(drj/dt)^2,j=1到3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=1到3求和},
4维时空速度矢量:
v(4)[1线矢]={va[a基矢],a=0到3求和}
=dr(4)[1线矢]/dt={dra[a基矢]/dt,a=0到3求和},
r0=ict,(光)、r0=ia*t,(声),
3维空间力矢量:
f(3)[1线矢]={fj[j基矢],j=1到3求和}
=dp(3)[1线矢]/dt={dpj[j基矢]/dt,j=1到3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=0到3求和},
v(4)={va^2,a=0到3求和}^(1/2)
=ic{1-(vj/c)^2,j=1到3求和}^(1/2), (光)、
=ia* {1-(vj/a*)^2,j=1到3求和}^(1/2), (声),
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=0到3求和},
p(4) =mdr(4) /dt=m{va^2,a=0到3求和}^(1/2)
=icm{1-(vj/c)^2,j=1到3求和}^(1/2), (光)、
=ia*m{1-(vj/a*)^2,j=1到3求和}^(1/2), (声),
当vj^2,j=1到3求和=0,令m=m0,有:
m=m0/{1-(vj/c)^2,j=1到3求和}^(1/2), (光)、
=m0/{1-(vj/a*)^2,j=1到3求和}^(1/2), (声)
4维时空力矢量:
f(4)[1线矢]= dp(4)[1线矢]/dt= {dpa[a基矢]/dt,a=0到3求和},
f(4)={fa^2,a=0到3求和}^(1/2)
=ic{1-(fj/c)^2,j=1到3求和}^(1/2), (光)、
=ia* {1-(fj/a*)^2,j=1到3求和}^(1/2), (声),
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), (光)、
=ia*{ (v0j)^2- (vkl /a*)^2,jkl=123循环求和}^(1/2), (声),
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), (光)、
=ia*m{ (v0j)^2- (vkl /a*)^2,jkl=123循环求和}^(1/2), (声),
当(vkl)^2,jkl=123循环求和=0,
令m{ (v0j)^2,j=1到3求和}^(1/2)=m0,有:
m==m0/{ (v0j)^2,j=1到3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), (光)、
=ia*{ (f0j)^2- (fkl /a*)^2,jkl=123循环求和}^(1/2), (声),
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) (光)、
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) (声),
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}(光)、
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}(声),
当(v0k,0l,jj/a*)^2,jkl=123循环求和=0,
令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) (光)、
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) (声),
(未完待续)
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