I've recently become fascinated by the geometry of curves, especially topics that involve rolling curves, trajectories, and dynamics within these structures. My interest started with some YouTube videos that delve into subjects like firing a laser within an ellipse and observing its path, as well as exploring various types of curves like cycloid. My background in calculus (particularly from studying Calculus II) has made me curious about the deeper mathematical principles behind these phenomena.
Is there a specific branch of mathematics that focuses on the study of such topics, like rolling curves or trajectories within curves? If so, what is it called, and what are the prerequisites for studying it? Additionally, could anyone recommend some comprehensive books or resources that cover this area in depth?
As a self-learner without access to formal classes, I would greatly appreciate any guidance on how to approach studying this field independently. Thank you in advance!
