diff --git a/examples/control/dynamics.py b/examples/control/dynamics.py
new file mode 100644
index 00000000..98ace94f
--- /dev/null
+++ b/examples/control/dynamics.py
@@ -0,0 +1,120 @@
+import jax.numpy as jnp
+import numpy as np
+
+from crazyflow.control import Control
+from crazyflow.control.transform import motor_force2rotor_vel
+from crazyflow.sim import Dynamics, Sim
+
+DURATION = 5.0
+FPS = 60
+TRAJECTORY_CENTER = np.array([0.0, 0.0, 1.0])
+TRAJECTORY_SIZE = np.array([1.0, 0.0, 0.5])
+
+
+def figure_eight(t: float) -> np.ndarray:
+    """Return the position, velocity, and acceleration reference at time ``t``."""
+    omega = 2.0 * np.pi / DURATION
+    phase = omega * t
+    cmd = np.zeros((1, 1, 13))
+    cmd[..., 0:3] = TRAJECTORY_CENTER + TRAJECTORY_SIZE * np.array(
+        [np.sin(phase), 0.0, np.sin(2.0 * phase)]
+    )
+    cmd[..., 3:6] = (
+        TRAJECTORY_SIZE * omega * np.array([np.cos(phase), 0.0, 2.0 * np.cos(2.0 * phase)])
+    )
+    cmd[..., 6:9] = (
+        -TRAJECTORY_SIZE * omega**2 * np.array([np.sin(phase), 0.0, 4.0 * np.sin(2.0 * phase)])
+    )
+    return cmd
+
+
+def reset_sim(sim: Sim) -> None:
+    """Reset a simulation to the initial reference state and hover rotor speed."""
+    sim.reset()
+    initial_state = figure_eight(0.0)
+    hover_thrust = sim.data.params.mass * -sim.data.params.gravity_vec[-1]
+
+    if sim.dynamics == Dynamics.first_principles:
+        motor_forces = jnp.broadcast_to(hover_thrust / 4.0, sim.data.states.rotor_vel.shape)
+        rotor_vel = motor_force2rotor_vel(motor_forces, sim.data.params.rpm2thrust)
+    elif sim.dynamics in (Dynamics.so_rpy_rotor, Dynamics.so_rpy_rotor_drag):
+        # These models store collective thrust in the shared rotor velocity state.
+        hover_state = (hover_thrust - sim.data.params.acc_coef) / sim.data.params.cmd_f_coef
+        rotor_vel = jnp.broadcast_to(hover_state, sim.data.states.rotor_vel.shape)
+    else:
+        # The rotor state is unused by so_rpy, but keep its reset state nonzero too.
+        rotor_vel = jnp.broadcast_to(hover_thrust, sim.data.states.rotor_vel.shape)
+
+    states = sim.data.states.replace(
+        pos=sim.data.states.pos.at[...].set(initial_state[..., 0:3]),
+        vel=sim.data.states.vel.at[...].set(initial_state[..., 3:6]),
+        rotor_vel=sim.data.states.rotor_vel.at[...].set(rotor_vel),
+    )
+    sim.data = sim.data.replace(states=states)
+
+
+def main(plot: bool = False, render: bool = False) -> None:
+    trajectories: dict[Dynamics, np.ndarray] = {}
+    rmses: dict[Dynamics, float] = {}
+    reference = np.empty((0, 3))
+
+    for dynamics in Dynamics:
+        sim = Sim(dynamics=dynamics, control=Control.state)
+        reset_sim(sim)
+
+        n_steps = int(DURATION * sim.control_freq)
+        times = np.arange(n_steps + 1) / sim.control_freq
+        commands = np.stack([figure_eight(t) for t in times])
+        reference = commands[:, 0, 0, 0:3]
+        trajectory = [np.asarray(sim.data.states.pos[0, 0])]
+
+        for i, cmd in enumerate(commands[1:]):
+            sim.state_control(cmd)
+            sim.step(sim.freq // sim.control_freq)
+            trajectory.append(np.asarray(sim.data.states.pos[0, 0]))
+            if ((i * FPS) % sim.control_freq) < FPS and render:
+                sim.render()
+
+        sim.close()
+        trajectory = np.asarray(trajectory)
+        trajectories[dynamics] = trajectory
+        rmses[dynamics] = np.sqrt(np.mean(np.sum((trajectory - reference) ** 2, axis=-1)))
+        print(f"{dynamics.value}: position RMSE = {rmses[dynamics]:.3f} m")
+
+    if plot:
+        plot_results(reference, trajectories, rmses)
+
+
+def plot_results(
+    reference: np.ndarray, trajectories: dict[Dynamics, np.ndarray], rmses: dict[Dynamics, float]
+) -> None:
+    """Plot the x-z trajectories and lateral positions against the reference."""
+    # Only import if plotting is desired to avoid a dependency on matplotlib.
+    import matplotlib.pyplot as plt
+
+    fig, (ax_xz, ax_y) = plt.subplots(1, 2, figsize=(12, 5), layout="constrained")
+    ax_xz.plot(reference[:, 0], reference[:, 2], "k--", linewidth=2, label="reference")
+    times = np.linspace(0.0, DURATION, len(reference))
+    ax_y.plot(times, reference[:, 1], "k--", linewidth=2, label="reference")
+    for dynamics, trajectory in trajectories.items():
+        label = f"{dynamics.value} (RMSE={rmses[dynamics] * 1_000:.0f}mm)"
+        ax_xz.plot(trajectory[:, 0], trajectory[:, 2], label=label)
+        ax_y.plot(times, trajectory[:, 1], label=label)
+
+    ax_xz.set_title("Figure-eight trajectory")
+    ax_xz.set_xlabel("x (m)")
+    ax_xz.set_ylabel("z (m)")
+    ax_xz.set_aspect("equal", adjustable="datalim")
+    ax_xz.legend()
+    ax_y.set_title("Out-of-plane position")
+    ax_y.set_xlabel("time (s)")
+    ax_y.set_ylabel("y (m)")
+    for ax in (ax_xz, ax_y):
+        ax.set_box_aspect(1)
+        ax.grid()
+    fig.suptitle("Figure-eight tracking across dynamics models")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main(plot=True, render=False)