The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
We find two new classes of precession motions of a gyrostat with fixed point. The motions are described by the Kirchhoff differential equations. For the first class, the velocities of precession and free rotation are equal and given in the form of a trigonometric polynomial of the first degree in the angle of free rotation. For the second class, the precession and rotation velocities do not coincide...
We investigate conditions for the existence of regular precessions of a gyrostat under the action of potential and gyroscopic forces under the assumption that the axis of precession does not coincide with the axis of symmetry of the force field. We find a solution of the Kirchhoff equation that contains one essential arbitrary constant.