Equations of motion and ballistic paths of volcanic ejecta

When the equations of motion are broken down into component form their solution provides the coordinates of positions of moving particles at successive times, making it possible to plot the paths of those particles. In two dimensions the equations contain horizontal and vertical accelerations which, when added separately in each component's direction, provide the net force per unit mass acting horizontally and vertically. Repeated integration of accelerations leads to particle velocities and displacements, hence particle positions and paths. Though conceptually applicable to many kinds of motion in geomorphology, the method is applied here to paths of volcanic ejecta in equatorial latitudes. The horizontal component includes the sum of inertial, resistance and aeolian terms whereas the vertical component is the sum of inertial, gravitational, resistance, lift and total centrifugal terms. The total centrifugal effect on a body in motion on a rotating Earth is itself composed of two components. One component is the conventionally conceived centrifugal effect at right angles to Earth's polar axis. The second component is the Coriolis effect at right angles to the velocity vectors that are tangential to the path of motion and at right angles to the axis of spin of the moving body. When the axis of spin is coincident with the polar axis, as it is for eastward motion of a body on the equator, both components act in the same direction, in this case upwards vertically. Completing the scenario is the inclusion of the equatorial tropopause which impedes further vertical motion but allows horizontal motion to continue, an aspect of considerable importance with respect to transport of dust (volcanic and aeolian) and pollutants.