diff --git a/course/lecture/lecture2.md b/course/lecture/lecture2.md
index 14b75ba3677076ca6764f668062987a2740b33a8..d337c4eff7051b845bb19d12340ac36567d451e5 100644
--- a/course/lecture/lecture2.md
+++ b/course/lecture/lecture2.md
@@ -5,6 +5,9 @@
 
 ------
 
+**_Contents_**
+
+[[_TOC_]]
 
 ## III) Indirect simple shooting
 
@@ -66,7 +69,7 @@ The *indirect simple shooting method* consists in solving this equation.
 
 >>>
 
-In order to solve the shooting equations, we need to compute the control law $u[\cdot]$, the Hamiltonian system $`\vec{H}`$ (or $`\vec{h}`$), we need an [integrator method](https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations) to compute the *exponential map* $\exp(t \vec{H})$ defined by
+In order to solve the shooting equations, we need to compute the control law $`u[\cdot]`$, the Hamiltonian system $`\vec{H}`$ (or $`\vec{h}`$), we need an [integrator method](https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations) to compute the *exponential map* $`\exp(t \vec{H})`$ defined by
 ```math
 \exp(t \vec{H})(x_0, p_0) := z(t, x_0, p_0),
 ```
@@ -77,3 +80,12 @@ and we need a [Newton-like](https://en.wikipedia.org/wiki/Newton%27s_method) sol
 **_Remark:_**
 It is important to understand that if $`(p_0^*, \lambda^*)`$ is solution of $`S=0`$, then the control $`u(\cdot) := u[z(\cdot, x_0, p_0^*)]`$ is a candidate as a solution of the optimal control problem. It is only a candidate and not a solution of the OCP since the PMP gives necessary conditions of optimality. We would have to go further to check  whether the control is locally or globally optimal.
 
+<div align="center">
+    <img src="attachment:21f9cc6f-5061-4fbe-ab9b-b905c2389dc9.png" width="400">
+</div>
+<div align="center">
+<i>
+Figure: Illustration of the shooting method in the state-time space. The blue trajectory reaches the target in red. The shooting method consists in finding the right impulse to reach the target.
+</i>
+</div>
+