2 ∫ 0 c Δ t 1 1 + ( a x c 2 + v c ) 2 d x + 2 ∫ 0 c Δ t 2 1 + ( a x c 2 + v + a Δ t 1 c ) 2 d x + ( 2 v + a ( Δ t ′ + Δ t 1 + Δ t 2 ) ) ( Δ t ′ − Δ t 1 − Δ t 2 ) = 2 c Δ t ′ {\displaystyle 2\int _{0}^{c\Delta t_{1}}{\sqrt {1+{({\frac {ax}{c^{2}}}+{\frac {v}{c}})}^{2}}}\,dx+2\int _{0}^{c\Delta t_{2}}{\sqrt {1+{({\frac {ax}{c^{2}}}+{\frac {v+a\Delta t_{1}}{c}})}^{2}}}\,dx+{(2v+a(\Delta t^{\prime }+\Delta t_{1}+\Delta t_{2}))(\Delta t^{\prime }-\Delta t_{1}-\Delta t_{2})}=2c\Delta t^{\prime }}
Δ t ′ = Δ t ( c 2 + v 2 − v c − v ) , M = m ( c 2 + v 2 − v c − v ) , L = l ( c − v c 2 + v 2 − v ) {\displaystyle \Delta t^{\prime }={\Delta t}\left({\frac {{\sqrt {c^{2}+v^{2}}}-v}{c-v}}\right),M=m\left({\frac {{\sqrt {c^{2}+v^{2}}}-v}{c-v}}\right),L=l\left({\frac {c-v}{{\sqrt {c^{2}+v^{2}}}-v}}\right)}
a = d v d t , F ≈ M a ( 1 + 3 v 2 c ) , P ≈ M v ( 1 + 3 v 4 c ) , E ≈ 1 2 M v 2 ( 1 + v c ) {\displaystyle a={\frac {dv}{dt}},F\approx Ma(1+{\frac {3v}{2c}}),P\approx Mv(1+{\frac {3v}{4c}}),E\approx {\frac {1}{2}}Mv^{2}(1+{\frac {v}{c}})}
