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  "body": "\n## Summary\n\nA hybrid system is a dynamical system whose state has a continuous part and a discrete part, called the mode.\nThe continuous part flows by [[ordinary differential equations|0NT64JV96A]], and the mode changes by jumps.\nIn each mode the continuous state follows its own [[vector field|0299VCW1TH]].\nWhen it reaches a switching condition, the mode changes and the continuous state may be reset.\nHybrid systems model mechanical systems with impacts, digital controllers acting on physical plants, and switching circuits.\n\n## Explanations\n\n### L1 human\n\nA thermostat is the classic picture.\nThe room temperature changes smoothly, but the heater is either on or off, and it switches when the temperature crosses a threshold.\nA bouncing ball is another example: it falls smoothly under gravity, and at each impact its velocity jumps from downward to upward.\nA hybrid system is any model that mixes such smooth motion with sudden switches.\n",
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