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Diffstat (limited to 'content/know/concept/legendre-transform/index.pdc')
| -rw-r--r-- | content/know/concept/legendre-transform/index.pdc | 9 |
1 files changed, 5 insertions, 4 deletions
diff --git a/content/know/concept/legendre-transform/index.pdc b/content/know/concept/legendre-transform/index.pdc index 290a89a..9cb6824 100644 --- a/content/know/concept/legendre-transform/index.pdc +++ b/content/know/concept/legendre-transform/index.pdc @@ -27,9 +27,9 @@ $$\begin{aligned} y(x) = f'(x_0) (x - x_0) + f(x_0) = f'(x_0) x - C \end{aligned}$$ -The Legendre transform $L(f')$ is defined such that $L(f'(x_0)) = C$ (or -sometimes $-C$ instead) for all $x_0 \in [a, b]$, where $C$ is the -constant corresponding to the tangent line at $x = x_0$. This yields: +The Legendre transform $L(f')$ is defined such that $L(f'(x_0)) = C$ +(or sometimes $-C$) for all $x_0 \in [a, b]$, +where $C$ corresponds to the tangent line at $x = x_0$. This yields: $$\begin{aligned} L(f'(x)) = f'(x) \: x - f(x) @@ -85,7 +85,8 @@ $$\begin{aligned} \end{aligned}$$ Legendre transformation is important in physics, -since it connects Lagrangian and Hamiltonian mechanics to each other. +since it connects [Lagrangian](/know/concept/lagrangian-mechanics/) +and Hamiltonian mechanics to each other. It is also used to convert between thermodynamic potentials. |