From 9507d93385b98c1452a3035a05008ad84008f74d Mon Sep 17 00:00:00 2001 From: flavis Date: Wed, 27 May 2020 10:25:05 +0200 Subject: [PATCH] add stupid calculations in la4 and update theo5 --- sose2020/la/uebungen/la4.pdf | Bin 99265 -> 113240 bytes sose2020/la/uebungen/la4.tex | 153 +++++++++++++++++++++++++++++++ sose2020/theo/uebungen/theo5.pdf | Bin 108982 -> 108671 bytes sose2020/theo/uebungen/theo5.tex | 7 +- 4 files changed, 157 insertions(+), 3 deletions(-) diff --git a/sose2020/la/uebungen/la4.pdf b/sose2020/la/uebungen/la4.pdf index a00a0aad9bd5b7a5941ef003745252a6d8fbd0f9..55df0e723552580139fae0dfdf94499f0f0ae448 100644 GIT binary patch delta 86289 zcmZ5`b8sch7i?_jh8x?qZCe}Lc5-9xZg6AUwrv|5TN`WRx8JW`)vJ1cP0!R+b$gap(~7wl&Cd?ERnTA^E!rBhD8Kzxc;fUc?`rsl~e z`{`%M9aS708BRvIuI@$##nEBZd*r7tE^P4rLMV@&iJ8HGk^t99!lgWr62xQFx=WUul&OYJXp3*E}pb{Ar=law90hg(m!%~&!}lVJAXJBR;I3H zR{HcA2$IOC3!ylVau#^mm>!Re<47MY%*8-xwZG#;>XI!AB86c}9e)D}CucGQX0qec zM~ANZS(-~>j91VW(jvJ`Bc0Ov0jDzbe>`s+jI*jK< 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\omega^2 \sin^2\vartheta + mgR\cos\vartheta + &= \frac{p_{\vartheta}^2}{2mR^2} - \frac{1}{2} R^2 \omega^2 \sin^2\vartheta + mgR\cos\vartheta .\end{align*} \item Es liegt hier zwar ein Potential vor, allerdings ist die kinetische Energie des Systems gegeben als @@ -47,8 +47,9 @@ an der zeitabhängigen Zwangsbedingung. Wegen $\frac{\partial H}{\partial t} = 0$ ist die Hamilton Funktion zeitlich - erhalten. Außerdem ist $\dot{w} = 0$, also ist das System - invariant gegenüber Zeittranslation. Damit folgt Energieerhaltung. + erhalten. Da die Zwangskräfte von der Zeit abhängen, ist das + System nicht invariant gegenüber Zeittranslation, also ist die Energie nicht + erhalten. \item Für die kanonischen Gleichungen folgt \begin{align*} \frac{\partial H}{\partial p_{\vartheta}} &= \frac{2 p_{\vartheta}}{mR^2} - \frac{p_{\vartheta}}{mR^2}