This example demonstrates how to model a hybrid system with discrete events (impacts) using Simit. A ball is dropped from a height, accelerates due to gravity, and bounces off the ground with a coefficient of restitution.

System Dynamics

The vertical position $y$ of the ball is governed by gravity $g$:

When the ball hits the ground ($y \le 0$), its velocity $v$ is reversed and dampened:

Where $e$ is the coefficient of restitution (between 0 and 1).

Block Diagram

To model this in Simit:

1. Integrator blocks are used to compute velocity $v$ from acceleration $a$, and position $y$ from velocity $v$.
2. A Constant block provides gravity $g = 9.81$.
3. A Zero Crossing or Hit Crossing detection logic (simulated via conditional logic in this basic example) handles the bounce.

Note: In the current version of Simit, we can model the impact using a logic block that resets the integrator state or applies an impulse force.

Step-by-Step Implementation

1. Add two Integrator blocks.
   • Integrator 1 (Velocity): Initial condition = $0$.
   • Integrator 2 (Position): Initial condition = $10$ (drop height).
2. Add a Gain block set to -9.81 (Gravity) feeding into Integrator 1.
3. Add a Scope to visualize position $y$.

(Full hybrid modeling features are coming in upcoming updates)

Simulation Results

Run the simulation for $10$ seconds. You will see the ball’s height parabolic trajectory decreasing with each bounce as energy is lost.