Applications of Three Dimensional Analytic Geometry

This volume focuses on seven applications of three dimensional analytic geometry to every day readily observable natural phenomena and on applications of three dimensional analytic geometry in new technologies such as Computer Aided Design (CAD) systems and animation and simulated motion of objects on television and motion picture screens. The reader will learn how the concepts of three dimensional analytic geometry are applied in science and how these concepts have been applied to create the new technologies of CAD and simulated motion of objects on a computer monitor screen.

In Chapter I applications of three dimensional analytic geometry in the field of optics are presented.

In Chapter II the trajectories of satellites, ballistic missiles, and artillery shells are all treated as elliptical trajectories. To obtain the familiar formulas for trajectories found in most physics texts, the conditions allowing approximation of elliptical orbits by parabolas are derived.

In Chapter III techniques of three dimensional analytic geometry are applied to deduce, for each of the four seasons, the hours of daylight and the Sun's elevation at Noon.

In Chapter IV three dimensional analytic geometry is applied to a calculation of the distribution of energy from the Sun over the surface of Earth and how that distribution is affected by a change in Earth's spin axis tilt. This is a pertinent topic, because a change in the spin axis angle can cause changes in the size if the polar ice caps.

The force of attraction on Earth's oceans of the Moon and the Sun causes the tides.

A particularly interesting application of three dimensional analytic geometry is the calculation of the acceleration of ocean waters caused by the Moon and the Sun is found in Chapter V. Not only does the Moon cause the tidal wave, it also causes stresses within Earth. The Earth, or any other planet, creates stress within their respective Moons. These effects are also illustrated in Chapter V.

Chapters VI and VII show how the basic concepts of three dimensional analytic geometry are used to create the new technologies of Computer Aided Design, and simulated motion and animation of objects as seen on computer monitors, television and motion picture screens. The basic requirements for software that allows one to draw simple objects is discussed and links to simulated motion of an airplane taking off and executing a circular climbing turn and a turn in a plane at fixed altitude are included.