# 理论物理学要点及其发展（63）

（接（62））

62．惯性力1线矢点乘微分位移1线矢相应的微分做功

=对该粒子动量 (P)的时间导数d (P)/dt

=d( m(0) (v)/(1-(v(3)/c)^2)^(1/2)/dt

= m(0)((d (v)/dt)/(1-(v(3)/c)^2)^(1/2)-1+(v(3)(dv(3)dt)/c ) (v)

/(1-(v(3)/c)^2)^(3/2)),

=作用于其上的惯性力 (f)沿位移d (r)方向所做的功，dA

= (f)d(r)的点乘积，(f)(点乘)d(r)

=m(0)((d(v)/dt)/(1-(v(3)/c)^2)^(1/2)

-1+(v(3)(dv(3)/dt)/c )(v)/(1-(v(3)/c)^2)^(3/2))(点乘)d(r)

=m(0)((d(v)/dt)/(1-(v(3)/c)^2)^(1/2)

-1+(v(3)dv(3)/c )(v)/(1-(v(3)/c)^2)^(3/2))(点乘)d(v)

=m(0)((d(v)(点乘)(v))(1-(v(3)/c)^2)^(1/2)

-1+(v(3)dv(3)/c )(v)(点乘)d(v)/(1-(v(3)/c)^2)^(3/2))

=m(0)((v(3)dv(3))(1-(v(3)/c)^2)^(1/2)

+(v(3)dv(3)/c)^2/(1-(v(3)/c)^2)^(3/2))

=m(0)(d(v(3)^2/2)(1-(v(3)/c)^2)^(1/2)

+(dv(3)^2/(2c))^2/(1-(v(3)/c)^2)^(3/2

=m(0)v(3)dv(3)/(1-(v(3)/c)^2)^(3/2)

=m(0)(dv(3)^2/2)/(1-(v(3)/c)^2)^(3/2),

(因有：d(r)/dt=(v), d(v)/dt(点乘)d(r)=d(v)(点乘)d(r)/dt=vdv

=-c^2+v(3)dv(3))

dm=d(m(0)/(1-(v(3)/c) ^ 2) ^(1/2)) =m(0)(2dv(3)^2/c^2)/(1-(v(3)/c)^2)^(3/2),

dE =dmc^2

c是常数，在惯性牵引运动系，m也是常数，即得：

E=mc^2，这就是爱因斯坦的质能关系式。(此处m显然是任何粒子的运动质量)

（未完待续）

http://blog.sciencenet.cn/blog-226-651973.html

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GMT+8, 2021-11-27 22:23