Motion in a high or low pressure system

show spring?

show forces?

v0=

s=

tstop=



Legend:

total accel.

"spring" accel.

Coriolis accel.


What is this?

A puck is attached to a device that delivers a radial force, either inward or outward, but independent of the length of the device. The force is analogous to that experienced by a parcel of air in a low or high pressure system, with concentric rings of isobars, equally spaced. Here the time scale has been made dimensionless using the Coriolis parameter. The length scale is the initial radial position of the puck. There is no friction.

The components of the equation of motion for the puck are:

dU/dτ= sX/R + V

dV/dτ= sY/R - U

where

R=sqrt(X2+Y2)

and s is the strength of the radial force, negative is inward and positive is outward. Can you write the above equations in polar coordinates?

The initial conditions are X=1, Y=0, U=0 and V=V0. For certain combinations of s and V0, the subsequent motion will be circular.