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+```c++
+for each time_step t:
+    for each pedestrian p:
+
+        reset_social_force(p)
+
+        // (1)
+        compute_acceleration_term(p)
+
+        // (2)
+        compute_repulsive_effects_from_pedestrians(p, pedestrians)
+
+        // (3)
+        compute_repulsive_effects_from_borders(p, board)
+
+    for each pedestrian p:
+        // next pos, desired dir, desired v, curr v
+        update_state(p)
+```
+
+
+(1) $\vec{F}_\alpha(\vec{v}_\alpha, v^0_\alpha \vec{e}_\alpha) \vec{e}_\alpha(t) = \frac{1}{\tau_\alpha}(v^0_\alpha \vec{e}_\alpha - \vec{v}_\alpha)$
+
+(2) $\sum_{\beta} \vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{\beta})$
+
+(3) $\sum_{B} \vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha} - \vec{r}_{B})$