edit
Mtg 1:
1-1 defined as (Meeting Number) - (Slide Number)
German Transrapid Emsland 500 km/h , youtube, Uploaded by TransrapidSupporter on Feb 14, 2007
y
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{\displaystyle y^{1}(t)=\ }
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{\displaystyle u^{1}(s,t)=\ }
u
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=
{\displaystyle u^{2}(s,t)=\ }
f
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{\displaystyle f(y^{1}(t),t)\ }
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∂
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{\displaystyle \displaystyle {\begin{aligned}{\frac {d}{dt}}f(y^{1}(t),t)={\frac {\partial f}{\partial s}}(y^{1}(t),t){\dot {y}}^{1}(t)+{\frac {\partial f}{\partial t}}(y^{1}(t),t)\end{aligned}}}
(1)
y
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{\displaystyle {\dot {y}}^{1}(t)={\frac {d}{dt}}y^{1}(t)\ }
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{\displaystyle {\frac {d}{dt}}f=f_{,s}(y^{1},t){\dot {y}}^{1}+f_{,t}(y^{1},t)}
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f
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s
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y
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+
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{\displaystyle \displaystyle {\begin{aligned}{\frac {d^{2}}{dt^{2}}}f=f_{,s}(y^{1},t){\ddot {y}}^{1}+f_{,ss}(y^{1},t)({\dot {y}}^{'})+2f_{,st}(y^{1},t){\dot {y}}^{1}+f_{,tt}(y^{1},t)\end{aligned}}}
(2)
y
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{\displaystyle {\dot {y}}^{'}={\dot {y}}^{2}}
Material time derivative - Continuum Mechanics
Reynolds transport theorem - Continuum Mechanics
c
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y
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c
2
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y
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y
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c
1
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y
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y
˙
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c
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y
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=
0
{\displaystyle \displaystyle {\begin{aligned}c_{3}(y',t){\ddot {y}}^{1}+c_{2}(y^{1},t)({\dot {y}}^{1})^{2}+c_{1}(y^{1},t){\dot {y}}^{1}+c_{0}(y^{1},t)=0\end{aligned}}}
(3)
is an example of a nonlinear ordinary differential equation (ODE)
