commit d45573342607ebfa2750df39eda5dce43249f0ed
parent 14feccb829aa79422992b1aa5ae03e0520b4389f
Author: minerva-jupiter <ryouturn@gmail.com>
Date: Sat, 13 Jun 2026 16:34:40 +0900
docs: wrap derivation section in details element in README
Diffstat:
1 file changed, 5 insertions(+), 0 deletions(-)
diff --git a/README.md b/README.md
@@ -18,6 +18,9 @@ Purpose of this repository is creating an expressive wind synthesizer, like real
This parts play a role of generating sounds like the reed on a saxophone or the lips on a trumpet.
+<details>
+<summary>TL;DR Derivation of the simulation formula</summary>
+
##### TL;DR Derivation of the simulation formula
###### 1. Formulation of the Equations of Motion in Continuous Time
@@ -96,3 +99,5 @@ When calculating the difference between the true value and the approximation (lo
$$\epsilon_{local} = I_{true} - I_{approx} = \left( \frac{1}{6} - \frac{1}{4} \right) \ddot{f}[n]T^3 + O(T^4) = -\frac{1}{12}\ddot{f}[n]T^3 + O(T^4)$$
Since the error per step is $O(T^3)$ (order 3), the cumulative total truncation error up to the time limit $t$ ($t/T$ steps) is $O(T^2)$ (order 2).
+
+</details>
