Abstract
Cycloidal paths are ubiquitous in physics. Here, we show that representative cycloidal paths in physics can be described as superpositions of translations and rotations of a point through space. Using this unifying principle, the parametric equations of the path of a point on a rolling disk are derived for rolling without slipping, rolling with frictionless slipping, and when kinetic solid-on-solid friction is present during rolling with slipping. In a similar way, the parametric equations versus time for the orbit with respect to a star of a moon in a circular orbit about a planet that is in a circular orbit about a star are derived, where the orbits are coplanar. The parametric equations versus time for the path of the magnetization vector during undamped electron-spin resonance are found using the same principle, which show that cycloidal paths can occur under specified conditions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
