This example is interactive. Click the play button on any cell to execute it, or run all cells in sequence.

Switched Bouncing Ball

This example demonstrates advanced event handling with multiple simultaneous events, event switching, and conditional event logic. The bouncing ball bounces on a table first, and then drops to the floor and continues to bounce there.

You can also find this example as a single file in the GitHub repository.

This example showcases:

- Multiple ZeroCrossing events tracking different conditions - Condition events for conditional logic (count-based switching) - Dynamic event activation/deactivation using on()/off() methods - Nonlinear friction forces modeled with the Function block

First let's import the Simulation and Connection classes along with the required blocks and event managers:

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System Dynamics

The ball experiences:

Gravitational acceleration downward
Quadratic air resistance (Newton's drag law)
Elastic bounces at MATHINLINE1ENDMATH (floor) and MATHINLINE2ENDMATH (ceiling)

The equation of motion is:

MATHDISPLAY0ENDMATH

where MATHINLINE3ENDMATH is the mass-normalized friction coefficient.

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Block Diagram Construction

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Event Managers

We define three events:

1. E1: Table bounce at $x = 0$ (ZeroCrossing) 2. E2: Floor bounce at $x = -5$ (ZeroCrossing) 3. E3: Conditional switch after 10 floor bounces (Condition)

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The third event uses the Condition event type, which triggers based on a boolean condition rather than a zero crossing. Here it counts table bounces and disables detection after 10 occurrences:

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The condition event checks if the table bounce event E1 has occurred 10 times. When this happens, it:

Disables table bounce tracking with E1.off()
Disables itself with E3.off()

After this point, only the flfoor bounce E2 remains active.

We initialize the simulation with the adaptive timestep RKBS32 solver (Runge-Kutta-Bogacki-Shampine 3(2) method) to enable backtracking for the event system to resolve event locations in time:

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12:44:08 - INFO - LOGGING (log: True)
12:44:08 - INFO - BLOCKS (total: 6, dynamic: 2, static: 4, eventful: 0)
12:44:08 - INFO - GRAPH (nodes: 6, edges: 6, alg. depth: 3, loop depth: 0, runtime: 0.076ms)

Now let's run the simulation:

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12:44:08 - INFO - STARTING -> TRANSIENT (Duration: 15.00s)
12:44:08 - INFO - --------------------   1% | 0.0s<0.1s | 2644.1 it/s
12:44:08 - INFO - ####----------------  20% | 0.0s<0.1s | 3588.5 it/s
12:44:08 - INFO - ########------------  40% | 0.1s<0.1s | 3833.1 it/s
12:44:08 - INFO - ############--------  60% | 0.1s<0.0s | 3502.6 it/s
12:44:08 - INFO - ################----  80% | 0.2s<0.0s | 3594.9 it/s
12:44:08 - INFO - #################### 100% | 0.3s<--:-- | 3937.0 it/s
12:44:08 - INFO - FINISHED -> TRANSIENT (total steps: 862, successful: 595, runtime: 255.70 ms)

Results

Let's plot the results with all three event types marked differently:

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Analysis

The plot reveals several interesting behaviors:

Initial phase: The ball bounces on the table floor (MATHINLINE0ENDMATH, dashed lines)
Switch event: After 10 table bounces, the conditional event triggers (solid vertical line)
Post-switch phase: Table bounces are no longer detected, so the ball passes through the table and falls to the floor where it continues to bounce
Energy dissipation: Due to air resistance, the amplitude decreases over time

This demonstrates how event logic can dynamically change system behavior during simulation, useful for:

Mode switching in control systems
Modeling wear or failure after a certain number of cycles
Implementing complex state machines

Event Counts

We can also check how many times each event occurred:

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Table bounces (E1): 10
Floor bounces (E2): 15
Switch events (E3): 1

As expected, E1 should have exactly 10 events (the trigger condition), E3 should have 1 event (when it disabled itself), and E2 will vary depending on the system dynamics.