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adtzlr committed May 12, 2023
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Expand Up @@ -23,7 +23,7 @@ A solution curve for `(n)` equilibrium equations `fun` in terms of `(n)` unknown

<img src="https://raw.githubusercontent.com/adtzlr/contique/main/test/test_archimedean_spiral.svg" width="75%">

Fig. 1 [Archimedean spiral](https://en.wikipedia.org/wiki/Archimedean_spiral) equation solved with [contique](https://github.com/adtzlr/contique/blob/main/test/test_archimedean_spiral.py)
Fig. 1 [Archimedean spiral](https://en.wikipedia.org/wiki/Archimedean_spiral) equation solved with [contique](https://github.com/adtzlr/contique/blob/main/tests/test_archimedean_spiral.py)

### Extended equilibrium equations
The `lpf` value is appended to the unknows `x` which gives the so-called extended unknowns `y = [x, lpf]`. One additional control equation is added to the equilibrium equations to ensure `(n+1)` equations in terms of `(n+1)` extended unknowns (see next section). This reduces the solution to a point on the initial solution curve.
Expand Down Expand Up @@ -133,6 +133,6 @@ plt.arrow(
plt.gca().set_aspect("equal")
```

<img src="https://raw.githubusercontent.com/adtzlr/contique/main/test/test_sincos.svg" width="75%">
<img src="https://raw.githubusercontent.com/adtzlr/contique/main/tests/test_sincos.svg" width="75%">

Fig. 2 Solution states of [equilibrium equations](https://github.com/adtzlr/contique/blob/main/test/test_sincos.py) solved with contique
Fig. 2 Solution states of [equilibrium equations](https://github.com/adtzlr/contique/blob/main/tests/test_sincos.py) solved with contique

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