### A note on inertial motion

#### Abstract

This note contains an investigation of the inertial motion on the sphere including all the terms of the Coriolis forces. The velocity vector has a zonal, a meridional and a height components. The time dependence of these components are calculated by a solution of the three velocity equations containing only the Coriolis’ terms, and the three-dimensional position vector is then calculated from the velocity vector. The results depend on the latitude of the starting position. For most starting positions it is a good approximation to consider the latitude as a constant, because the results show that the south-north variations are quite small for reasonable values of the initial velocity vector which may be considered as the a-geostrophic wind and thus quite small. These remarks will be considered in detail in the paper. For each case the initial velocity vector (u

_{o}, v_{o}, w_{o}) and the starting position (x_{o}, y_{o}, z_{o}) are given. However, due to the nature of the Coriolis terms it is seen that the vertical component (w_{o}) cannot be given an arbitrary value since it is related to the other two components. The first step is to determine the time variations of the three velocity components, whereafter the trajectory of the three dimensional motion is determined.