Why can't trajectories in phase space intersect?
A phase space trajectory is a graphical representation of the path that a system takes through its phase space, which is a mathematical space that describes all possible states of a physical system.
A regular trajectory describes the physical path of an object in space, while a phase space trajectory describes the evolution of a system's state over time.
A phase space trajectory can provide insights into the behavior and stability of a system, as well as its energy and other physical properties.
Phase space trajectories are commonly used in fields such as physics, engineering, and biology to model and analyze complex systems, including celestial bodies, chemical reactions, and biological processes.
Phase space trajectories are typically plotted on a graph with the system's state variables as axes, and the trajectory is traced as the system evolves over time. This can also be done in higher dimensions using computer software.