Describe the fundamental operational principles of Positive Train Control (PTC) systems, including how track authority, speed restrictions, and train location data are continuously managed and enforced to prevent specific types of train collisions or overspeed events.

Positive Train Control (PTC) systems are advanced command, control, and communications systems designed to enhance railway safety by continuously monitoring and enforcing train movements. The fundamental operational principle of PTC is to prevent specific types of accidents, primarily train-to-train collisions, overspeed derailments, incursions into work zones, and movement through misaligned switches. This is achieved through the integration of four key elements: a robust communication network, a precise positioning system, a back office system, and onboard train systems, all working to manage and enforce track authority, speed restrictions, and train location data. Track authority, which is the permission for a train to occupy a specific section of track up to a defined limit, is continuously managed by the Back Office System. This central system maintains a real-time view of all train movements, track conditions, and dispatching orders. It calculates and issues track authority to each train's onboard PTC system via the communication network. The onboard PTC system on the train continuo....