Designbug in der Breite

Vielleicht lioegt das hierdran?
Originalbeitrag: https://www.mikrocontroller.net/topic/goto_post/5379491

$$dA=|dv1||dv2||sin??|=|dv1||dv2|1−cos2??=|dv1|2|dv2|2−|dv1|2|dv2|2cos2??=(dv1⋅dv1)(dv2⋅dv2)−(dv1⋅dv2)2dA=|dv1||dv2||sinϕ|=|dv1||dv2|1−cos2ϕ−−−−−−−−√=|dv1|2|dv2|2−|dv1|2|dv2|2cos2ϕ−−−−−−−−−−−−−−−−−−−−−−−−−√=(dv1⋅dv1)(dv2⋅dv2)−(dv1⋅dv2)2−−−−−−−−−−−−−−−−−−−−−−−−−−−√dA=|dv1||dv2||sinϕ|=|dv1||dv2|1−cos2ϕ−−−−−−−−√=|dv1|2|dv2|2−|dv1|2|dv2|2cos2ϕ−−−−−−−−−−−−−−−−−−−−−−−−−√=(dv1⋅dv1)(dv2⋅dv2)−(dv1⋅dv2)2−−−−−−−−−−−−−−−−−−−−−−−−−−−√ A=?dtds(?Xµ?t?Xµ?s)2−(?Xµ?t)2(?Xµ?s)2=?dtds−det(?Xµ?s1?X??s2?µ?)A=∫dτdσ(∂Xμ∂τ∂Xμ∂σ)2−(∂Xμ∂τ)2(∂Xμ∂σ)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=∫dτdσ−det(∂Xμ∂σ1∂Xν∂σ2ημν)−−−−−−−−−−−−−−−−−−√A=∫dτdσ(∂Xμ∂τ∂Xμ∂σ)2−(∂Xμ∂τ)2(∂Xμ∂σ)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=∫dτdσ−det(∂Xμ∂σ1∂Xν∂σ2ημν)−−−−−−−−−−−−−−−−−−√ S=−Tsc?titfdt?0smds(X?⋅X′)2−X?2X′2S=−Tsc∫τfτidτ∫σm0dσ(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√S=−Tsc∫τfτidτ∫σm0dσ(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√L(Xµ?,Xµ′)=(X?⋅X′)2−X?2X′2L(Xμ˙,Xμ′)=(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√L(Xμ˙,Xμ′)=(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√X?=?Xµ?t,X′=?Xµ?sX˙=∂Xμ∂τ,X′=∂Xμ∂σX˙=∂Xμ∂τ,X′=∂Xμ∂σ Pµt=?L?Xµ?=−Tsc(X?⋅X′)Xµ′−X′2X?µ(X?⋅X′)2−X?2X′2Pτμ=∂L∂Xμ˙=−Tsc(X˙⋅X′)X′μ−X′2X˙μ(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√Pτμ=∂L∂Xμ˙=−Tsc(X˙⋅X′)X′μ−X′2X˙μ(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√ Pµs=?L?Xµ′=−Tsc(X?⋅X′)X?µ−(X?)2Xµ′(X?⋅X′)2−X?2X′2Pσμ=∂L∂Xμ′=−Tsc(X˙⋅X′)X˙μ−(X˙)2X′μ(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√Pσμ=∂L∂Xμ′=−Tsc(X˙⋅X′)X˙μ−(X˙)2X′μ(X˙⋅X′)2−X˙2X′2−−−−−−−−−−−−−−−√ ?=det(?aß)γ=det(γαβ)γ=det(γαβ),imDetail?aß=(X?2X?X′X?X′X′2)γαβ=(X˙2X˙X′X˙X′X′2)γαβ=(X˙2X˙X′X˙X′X′2). S=Tsc?dtds−?S=Tsc∫dτdσ−γ−−−√S=Tsc∫dτdσ−γ−−−√ S=−m?ds=−m?−?µ?dXµdX?=−m?−?µ?dXµdtdX?dtdtS=−m∫ds=−m∫−ημνdXμdXν−−−−−−−−−−−√=−m∫−ημνdXμdτdXνdτ−−−−−−−−−−−√dτS=−m∫ds=−m∫−ημνdXμdXν−−−−−−−−−−−√=−m∫−ημνdXμdτdXνdτ−−−−−−−−−−−√dτ Ss=−T2?d2s−hhaß?aX⋅?ßXSσ=−T2∫d2σ −h−−−√hαβ∂αX⋅∂βXSσ=−T2∫d2σ −h−−−√hαβ∂αX⋅∂βX, haß(s,t)hαβ(σ,τ)hαβ(σ,τ)(d2s=dsdtd2σ=dσdτd2σ=dσdτ).Hilfsfeldalshaß=(−1001)hαβ=(−1001)hαβ=(−1001) S=T2?d2s(X?2−X′2)S=T2∫d2σ(X˙2−X′2)S=T2∫d2σ(X˙2−X′2) dXµ=a?µX?+bµδXμ=aμνXν+bμδXμ=aμνXν+bμmitdhaß=0δhαβ=0δhαβ=0. sa?fa(s)=s′aσα↦fα(σ)=σ′ασα↦fα(σ)=σ′αundhaß(s)=?f??sa?fd?sßh?d(s′)hαβ(σ)=∂fγ∂σα∂fδ∂σβhγδ(σ′)hαβ(σ)=∂fγ∂σα∂fδ∂σβhγδ(σ′). haß?e?(s,t)haßhαβ↦eϕ(σ,τ)hαβhαβ↦eϕ(σ,τ)hαβunddXµ=0δXμ=0δXμ=0. ?a?aXµ=0∂α∂αXμ=0∂α∂αXμ=0, Xµ(s,t)=Xµ(s+p,t)Xμ(σ,τ)=Xμ(σ+π,τ)Xμ(σ,τ)=Xμ(σ+π,τ). Xµ′=0X′μ=0X′μ=0fürs=0,pσ=0,πσ=0,π, Xµ|s=0=X0µXμ|σ=0=Xμ0Xμ|σ=0=Xμ0undXµ|s=p=XpµXμ|σ=π=XμπXμ|σ=π=Xμπ. s±=t±sσ±=τ±σσ±=τ±σmitAbleitungen?±=12(?t±?s)∂±=12(∂τ±∂σ)∂±=12(∂τ±∂σ)undWellengleichung?+?−Xµ=0∂+∂−Xμ=0∂+∂−Xμ=$$

Oh, Danke! Habe den Thread nicht durchgescrollt, sorry.

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Vielen Dank!

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