commit ff1fb593d1d975e0c5d5df7a1815949dc8ac338c
parent 1f3fc0545725ededf992f084d5779dff774d7988
Author: minerva-jupiter <ryouturn@gmail.com>
Date: Sat, 13 Jun 2026 16:37:03 +0900
docs: improve formatting of mathematical equations in README
Add missing newlines around math blocks to ensure proper rendering in Markdown.
Diffstat:
1 file changed, 4 insertions(+), 0 deletions(-)
diff --git a/README.md b/README.md
@@ -41,17 +41,21 @@ Let the sampling period be $T$, and consider the integral from continuous time t
The essence of the bilinear transform is to approximate the integrand using a trapezoidal approximation (multiplying the mean value at both ends by the interval width $T$) for the integral from time $(n-1)T$ to $nT$.
Discretization of position $x[n]$
+
```math
\int_{(n-1)T}^{nT} \frac{dx(t)}{dt} dt = \int_{(n-1)T}^{nT} v(t) dt
x[n] - x[n-1] = \frac{T}{2} \left( v[n] + v[n-1] \right) \quad \cdots \text{(Equation 1)}
```
+
Discretization of velocity $v[n]$
+
```math
\int_{(n-1)T}^{nT} \frac{dv(t)}{dt} dt = \int_{(n-1)T}^{nT} \frac{1}{m} \left( F(t) - r v(t) - k x(t) \right) dt
v[n] - v[n-1] = \frac{T}{2m} \left( F[n] + F[n-1] - r(v[n] + v[n-1]) - k(x[n] + x[n-1]) \right) \quad \cdots \text{(Equation 2)}
```
+
---
###### 3. Resolving the Algebraic Loop and Deriving the Simulation Formula
