Solutions with invariant ratios for certain problems of solidbody dynamics
Abstract
Papers relating to the construction and analysis of exact solutions of the equations of motion of a solid body and systems of solid bodies are discussed with emphasis on the method of invariant ratios for constructing the solutions and the hodographic method for studying the motion of a body. A review is presented of the exact solutions of the equations of motion for a gyrostat in a homogeneous force field. The problem of constructing solutions with two and three linear invariant ratios is solved in full, and the construction of solutions with one invariant ratio is completed in the case where the center of mass pertains to the principal plane of the ellipsoid of gyration. It is shown that the presence of a quadratic ratio makes it possible to reduce the problem to quadratures in the case of motion due to inertia. All solutions obtained with quadratic ratios are discussed, and such solutions are obtained by a uniform method on the basis of a single integrodifferential equation.
 Publication:

In: The history of the mechanics of gyroscopic systems. (A7539845 1935) Moscow
 Pub Date:
 1975
 Bibcode:
 1975hmgs.rept....5K
 Keywords:

 Body Kinematics;
 Dynamic Stability;
 Gyrostabilizers;
 Hodographs;
 Equations Of Motion;
 Invariance;
 Quadratures;
 Physics (General)