新古典力学 - 科学の基礎研究
An/An+1=1/rAn+1=rAnAn+1=rAnrAn=An+1r=An+1/AnFrFhFlFsFdFxFyFz(1/2)mvvL=U-KE=U+K物体ぶったいエネルギー距離きょり速度そくど位置いち運動うんどうここからFr(Fr)'=F'r+FvFh(Fh
An/An+1=1/rAn+1=rAnAn+1=rAnrAn=An+1r=An+1/AnFrFhFlFsFdFxFyFz(1/2)mvvL=U-KE=U+K物体ぶったいエネルギー距離きょり速度そくど位置いち運動うんどうここからFr(Fr)'=F'r+FvFh(Fh
ta;t-ΣFvΔtFl-(1/2)mvv=ΣF'lΔtU=FlK=(1/2)mvvU-K=Fl-(1/2)mvvL=U-KL=U-K=Fl-(1/2)mvvFl-(1/2)mvv=ΣF'lΔ
どうエネルギー最初は(Fx)=(Fx)(1/2)(mvv)=(1/2)(mvv)最後はS=ΣLΔt=Σ(U-K)Δt=Σ[Fx-(1/2)mvv]Δt=ΣΣF'xΔ
An+1=A1[(r^n)]An/An+1=1/rAn+1=rAnAn+1=rAnrAn=An+1r=An+1/AnFx(1/2)mvvL=U-KE=U+K物体ぶったいエネルギー距離きょり速度そくど位置いち運動うんどうここからFx(Fx)'=F'x+Fvy=fgy
ta;t-ΣFvΔtFd-(1/2)mvv=ΣF'dΔtU=FdK=(1/2)mvvU-K=Fd-(1/2)mvvL=U-KL=U-K=Fd-(1/2)mvvFd-(1/2)mvv=ΣF'dΔ
ta;t-ΣFvΔtFs-(1/2)mvv=ΣF'sΔtU=FsK=(1/2)mvvU-K=Fs-(1/2)mvvL=U-KL=U-K=Fs-(1/2)mvvFs-(1/2)mvv=ΣF'sΔ
ta;t-ΣFvΔtFz-(1/2)mvv=ΣF'zΔtU=FzK=(1/2)mvvU-K=Fz-(1/2)mvvL=U-KL=U-K=Fz-(1/2)mvvFz-(1/2)mvv=ΣF'zΔ
ta;t-ΣFvΔtFy-(1/2)mvv=ΣF'yΔtU=FyK=(1/2)mvvU-K=Fy-(1/2)mvvL=U-KL=U-K=Fy-(1/2)mvvFy-(1/2)mvv=ΣF'yΔ
ΔtラグランジアンLagrangianFx=Fx(1/2)mvv=(1/2)mvvFx-(1/2)mvv=Fx-(1/2)mvvU=UK=KU-K=U-KL=LL=U-KL=LLΔt=LΔtΣLΔt=ΣLΔtS=SS=ΣLΔtFx-(1/2)mvv=Fx-(1/2)mvvU-K=
Mm/r)'ΔtΣF'rΔt=Σ(GMm/r)'ΔtL=U-K=Fr-(1/2)mvv=ΣF'rΔtL=U-K=Fr-(1/2)mvv=ΣF'r
Lagrangian(Fx)=(Fx)Fx=Fx(1/2)mvv=(1/2)mvvFx-(1/2)mvv=Fx-(1/2)mvvU=UK=KU-K=U-KL=LLΔt=LΔtΣLΔt=ΣLΔtS=SFx-(1/2)mvv=Fx-(1/2)mvvU-K=U-KU-K=Fx-(1/2
1)]An+1=A1[(r^n)]An/An+1=1/rAn+1=rAnAn+1=rAnrAn=An+1r=An+1/Anオイラーの公式L=U-K=0LagrangianラグランジアンL=U-KU=FrK=(1/2)mvvL=U-K=Fr-(1/2)mvvE+(1/2)mvv=C
=nΣF'xΔt=nFx-(1/2)mvv=ΣF'xΔtFx-(1/2)mvv=ΣF'xΔt=nFx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2)mvvL=U-K=Fx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2)mvv=nL=U-K=ΣF'x
=nΣF'xΔt=nFx-(1/2)mvv=ΣF'xΔtFx-(1/2)mvv=ΣF'xΔt=nFx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2)mvvL=U-K=Fx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2)mvv=nL=U-K=ΣF'x
1/2)mvv=ΣF'xΔt=nFx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2)mvvL=U-K=Fx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2
1/2)mvv=ΣF'xΔt=nFx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2)mvvL=U-K=Fx-(1/2)mvv=ΣF'xΔt=nL=U-K=Fx-(1/2
)mvv=ΣFvΔtFx-(1/2)mvv=ΣF'xΔtU=FxK=(1/2)mvvU-K=Fx-(1/2)mvvL=U-KL=U-K=Fx-(1/2)mvvFx-(1/2)mvv=ΣF'xΔ
Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1L=U-K=Fr-(1/2)mvv=ΣF'rΔtΔLn=-ΔLn+1Δ[ΣLΔt]n=-Δ[ΣLΔt]n+1δ[ΣLΔt]n=-δ[ΣLΔt]n
Delta;[Fr-(1/2)mvv]n+1Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1L=U-K=Fr-(1/2)mvv=ΣF'rΔtΔLn=-ΔLn+1Δ[&S
Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1L=U-K=Fr-(1/2)mvv=ΣF'rΔtΔLn=-ΔLn+1Δ[ΣLΔt]n=-Δ[ΣLΔt]n+1δ[ΣLΔt]n=-δ[ΣLΔt]n
Delta;[Fr-(1/2)mvv]n+1Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1L=U-K=Fr-(1/2)mvv=ΣF'rΔtΔLn=-ΔLn+1Δ[&S
Delta;[Fr-(1/2)mvv]n+1Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1L=U-K=Fr-(1/2)mvv=ΣF'rΔtΔLn=-ΔLn+1Δ[&S
Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1Δ[Fr-(1/2)mvv]n=-Δ[Fr-(1/2)mvv]n+1L=U-K=Fr-(1/2)mvv=ΣF'rΔtΔLn=-ΔLn+1Δ[ΣLΔt]n=-Δ[ΣLΔt]n+1δ[ΣLΔt]n=-δ[ΣLΔt]n
≠CΣF'xΔt≠CFx-(1/2)mvv=ΣF'xΔtFx-(1/2)mvv=ΣF'xΔt≠CFx-(1/2)mvv=ΣF'xΔt≠CL=U-K=Fx-(1/2)mvvL=U-K=Fx-(1/2)mvv=ΣF'xΔt≠CL=Fx-(1/2)mvv=ΣF'xΔt≠CL=Fx-(1
Δ[Fx-(1/2)mvv]n=-Δ[Fx-(1/2)mvv]n+1Δ[Fx-(1/2)mvv]n=-Δ[Fx-(1/2)mvv]n+1L=U-K=Fx-(1/2)mvv=ΣF'xΔtΔLn=-ΔLn+1Δ[ΣLΔt]n=-Δ[ΣLΔt]n+1δ[ΣLΔt]n=-δ[ΣLΔt]n
vΔt-(F'xΔt+FvΔt)mvv-ΔFx=-2ΣFvΔt-F'xΔt-FvΔtPV/T=PV/TS=lnTΔS=ΔlnTE=U+KL=U-K(-L)=K-US=(1/2)rvsinθS=S(1/2)rvsinθ=(1/2)rvsinθrvsinθ=rvsinθF=FFrvs
vΔt-(F'xΔt+FvΔt)mvv-ΔFx=-2ΣFvΔt-F'xΔt-FvΔtPV/T=PV/TS=lnTΔS=ΔlnTE=U+KL=U-K(-L)=K-UΔS/Δt=(1/2)rvsinθΔS/Δt=ΔS/Δt(1/2)rvsinθ=(1/2)rvsinθrvsinθ=r
vΔt-(F'xΔt+FvΔt)mvv-ΔFx=-2ΣFvΔt-F'xΔt-FvΔtPV/T=PV/TS=lnTΔS=ΔlnTE=U+KL=U-K(-L)=K-UΔS/Δt=(1/2)rvsinθΔS/Δt=ΔS/Δt(1/2)rvsinθ=(1/2)rvsinθrvsinθ=r