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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present an integrable nonholonomic case of rolling without sliding of agyroscopic ball over a sphere. This case was introduced and studied in detailby Vasilije Demchenko in his 1923 doctoral dissertation defended at theUniversity of Belgrade, with Anton Bilimovic as the advisor. These results areabsolutely unknown to modern researchers. The study is based on the C. Neumanncoordinates and the Voronec principle. By using involved technique of ellipticfunctions, a detailed study of motion is performed. Several special classes oftrajectories are distinguished, including regular and pseudo-regularprecessions. So-called remarkable trajectories, introduced by Paul Painleve andAnton Bilimovic, are described in the present case. The historic context aswell as the place of the results in contemporary mechanics are outlined.

Demchenko's nonholonomic case of gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis