Abstract
This paper investigates the rolling without slipping of a homogeneous heavy ball on the surface of a rotating cone in two settings: without dissipation in a nonholonomic setting and with rolling friction torque which is proportional to the angular velocity of the ball. In the nonholonomic setting, the resulting system of five differential equations on the level set of first integrals is reduced to quadratures. A bifurcation analysis of the above system is carried out to determine the possible types of motion. In the second case, it is shown that there are not only trajectories emanating from the lower point of the cone (its vertex), but also trajectories to the vertex of the cone (fall). An analysis of the dependence of the type of terminal motion of the center of mass of the ball on initial conditions is carried out.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.