The motion of a mass undergoing free horizontal motion on a planets surface is analyzed in an inertial frame by using a potential well presentation. The following results from the conventional analysis in rotating coordinates are also found in inertial coordinates. Under typical circumstances the mass oscillates about the latitude where its angular momentum per unit mass matches that of the planet’s surface. For masses with nonzero angular momentum, conservation of angular momentum bounds the mass away from the pole. Motion with zero angular momentum is confined to a fixed meridian plane on which the mass may oscillate across the pole. Motion across the equator is possible only for masses with sufficient energy. Masses with angular momentum per unit mass greater than that of the planet at the equator oscillate about the equator with a limiting period determined by the excess angular momentum.
Received: June 18, 2014; Final Form: September 5, 2014
Corresponding author address: Norman Phillips, 18 Edward Lane, Merrimack, NH 03054. E-mail: napmar18@comcast.net
关于Norman Phillips的介绍：
NORMAN PHILLIPS IS a theoretical meteorologist who pioneered the use of numerical methods for the prediction of weather and climate changes. His influential studies led to the first computer models of weather and climate, as well as to an understanding of the general circulation of the atmosphere, including the transports of heat and moisture that determine the Earths climate. His 1955 model is generally regarded as a groundbreaking device that helped to win scientific skepticism in reproducing the patterns of wind and pressure of the entire atmosphere within a computer model.
Phillips received his B.S. from the University of Chicago in 1947 and his Ph.D. in 1951. He was the first to show, with a simple general circulation model, that weather prediction with numerical models was possible. The advent of numerical weather predictions in the 1950s also marked the transformation of weather forecasting from a highly individualistic effort to a cooperative task in which teams of experts developed complex computer programs. With the first digital computer in the 1950s, scientists tried to represent the complexity of the atmosphere and its circulation in numerical equations. Nineteenth- and early 20th century mathematicians such as Vilhelm Bjerknes and Lewis Fry Richardson had failed to come up with adequate mathematical models. Through the 1950s, some leading meteorologists tried to replace Bjerknes and Richardsons numerical approach with methods based on mathematical functions, working with simplified forms of the physics equations that described the entire global atmosphere. They succeeded in getting only partial mathematical models. These reproduced some features of atmospheric layers, but they could not show persuasively the features of the general circulation. Their suggested solutions contained instabilities as they could not account for eddies and other crucial features. Discouraged by such failures, scientists began to think that the real atmosphere was too complex to be described by a few lines of mathematics. The comment of such a leading climatologist as Bert Bolin is revealing of this skepticism. In 1952 Bolin argued that there was very little hope for the possibility of deducing a theory for the general circulation of the atmosphere from the complete hydrodynamic and thermodynamic equations. Yet, computers opened up new possibilities in the field, although the first digital specimens were extremely slow and often broke down.
