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author | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
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committer | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
commit | 61b5ce20f25c5785e41574998a12c6d06eb05a5e (patch) | |
tree | 20e2225b4f30b15d8dee30351041d1f33d42b34a /src/math/variation.org | |
parent | 561bac75579391c14e47eaccfabdf9eda98855da (diff) |
Diffstat (limited to 'src/math/variation.org')
-rw-r--r-- | src/math/variation.org | 19 |
1 files changed, 19 insertions, 0 deletions
diff --git a/src/math/variation.org b/src/math/variation.org new file mode 100644 index 0000000..fcbfb14 --- /dev/null +++ b/src/math/variation.org @@ -0,0 +1,19 @@ +#+title:Variation Calculus +#+author: Thomas Albers Raviola +#+date: 2022-10-01 +#+setupfile: ../../math_options.org + +* Disclaimer +This site as of now just a technology demonstration and its claims +should not be taken as true (even though I myself am pretty confident +they are) + +* Beltrami identity +\begin{align*} +\deriv{}{x}\pderiv{F}{\dot{y}} &= \pderiv{F}{y}\\ +\deriv{}{x}\left(\pderiv{F}{\dot{y}}\right)\deriv{y}{x} &= \pderiv{F}{y}\deriv{y}{x}\\ +\deriv{}{x}\left(\pderiv{F}{\dot{y}}\right)\deriv{y}{x} + \pderiv{F}{\dot{y}}\deriv{\dot{y}}{x} + \pderiv{F}{x} &= \pderiv{F}{y}\deriv{y}{x} + \pderiv{F}{\dot{y}} \deriv{\dot{y}}{x} + \pderiv{F}{x}\\ +\deriv{}{x}\left(\pderiv{F}{\dot{y}}\dot{y}\right) + \pderiv{F}{x} &= \deriv{F}{x}\\ +\deriv{}{x}\left(\pderiv{F}{\dot{y}}\dot{y} - F\right) &= - \pderiv{F}{x}\\ +\pderiv{F}{\dot{y}}\dot{y} - F\right &= C +\end{align*} |