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        "%matplotlib inline"
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      "source": [
        "\nExample demonstrating when and how to identify model state limits. \n"
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      "source": [
        "from progpy.models.thrown_object import ThrownObject\nfrom math import inf\n\ndef run_example():\n    # Demo model\n    # Step 1: Create instance of model (without drag)\n    m = ThrownObject( cd = 0 )\n\n    # Step 2: Setup for simulation \n    def future_load(t, x=None):\n        return {}\n\n    # add state limits\n    m.state_limits = {\n        # object may not go below ground height\n        'x': (0, inf),\n\n        # object may not exceed the speed of light\n        'v': (-299792458, 299792458)\n    }\n\n    # Step 3: Simulate to impact\n    event = 'impact'\n    simulated_results = m.simulate_to_threshold(future_load, threshold_keys=[event], dt=0.005, save_freq=1)\n    \n    # Print states\n    print('Example 1')\n    for i, state in enumerate(simulated_results.states):\n        print(f'State {i}: {state}')\n    print()\n\n    # Let's try setting x to a number outside of its bounds\n    x0 = m.initialize(u = {}, z = {})\n    x0['x'] = -1\n\n    simulated_results = m.simulate_to_threshold(future_load, threshold_keys=[event], dt=0.005, save_freq=1, x = x0)\n\n    # Print states\n    print('Example 2')\n    for i, state in enumerate(simulated_results.states):\n        print('State ', i, ': ', state)\n    print()\n\n    # Let's see what happens when the objects speed aproaches its limit\n    x0 = m.initialize(u = {}, z = {})\n    x0['x'] = 1000000000\n    x0['v'] = 0\n    m.parameters['g'] = -50000000\n    \n    print('Example 3')\n    simulated_results = m.simulate_to_threshold(future_load, threshold_keys=[event], dt=0.005, save_freq=0.3, x = x0, print = True, progress = False)\n\n    # Note that the limits can also be applied manually using the apply_limits function\n    print('limiting states')\n    x = {'x': -5, 'v': 3e8}  # Too fast and below the ground\n    print('\\t Pre-limit: {}'.format(x))\n    x = m.apply_limits(x)\n    print('\\t Post-limit: {}'.format(x))\n\n# This allows the module to be executed directly \nif __name__=='__main__':\n    run_example()"
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