Notes on the Motion of a Rotating Solid Cylinder on a Rotaing Earth

[摘要] In the present paper, an exact formulation of the problem of the motion of a rotating solid cylinder on a rotating earth is attempted by means of the Hamiltonian equations of motion. The theorems of the conservation of angular momenta, about the polar axis and about the vertical axis of the cylinder, and of the total energy are obtained as the results of three intermediate integrals. From these integrals, the equations of motion of the cylinder are examined. In addition to the force acting upon the cylinder endowed with given amounts of relative vorticity, first noticed by Rossby, the inertia force acting upon the cylinder is separated, and the importance of this force is emphasized. Such results are in accord with those obtained by Syono in another way.

[学科分类] 大气科学