English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider two types of trajectories found in a wide range of mechanicalsystems, viz. box orbits and loop orbits. We elucidate the dynamics of theseorbits in the simple context of a perturbed harmonic oscillator in twodimensions. We then examine the small-amplitude motion of a rigid body, therock'n'roller, a sphere with eccentric distribution of mass. The equations ofmotion are expressed in quaternionic form and a complete analytical solution isobtained. Both types of orbit, boxes and loops, are found, the particular formdepending on the initial conditions. We interpret the motion in terms ofepi-elliptic orbits. The phenomenon of recession, or reversal of precession, isassociated with box orbits. The small-amplitude solutions for the symmetriccase, or Routh sphere, are expressed explicitly in terms of epicycles; there isno recession in this case.

Quaternion Solution for the Rock'n'roller: Box Orbits, Loop Orbits and Recession