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Simulation loop
In every case we will have to:
- Compute the Jacobian
-- Uses a velocity bias to prevent drift/stretching (Baumgarte stabilization): $$b = \frac{\beta}{t} \cdot C$$
-- Compute the inverse of $JM^{-1}J^T$ (this is why we want smaller jacobians).
-- Compute lagrange multipliers (anything that multiplies a derivative that points in the direction we want is called a lagrange multiplier, this is just to scare people).
+- Use a velocity bias to prevent drift/stretching (Baumgarte stabilization): $$b = \frac{\beta}{t} \cdot C$$
+- Compute the inverse of $JM^{-1}J^T$ (this is why we want smaller Jacobians).
+- Compute Lagrange multipliers (anything that multiplies a derivative that points in the direction we want is called a Lagrange multiplier, this is just to scare people).
$$\lambda = -\frac{J \cdot v_{tentative} + b}{JM^{-1}J^T}$$
-- And the velocity gets corrected(so it meets the constraints) by applying:
+- And the velocity gets corrected (so it meets the constraints) by applying:
$$v_f = v_{tentative} + \lambda J^T$$
Rendering: Draws particles and links.