Quasi-Spherical Orbits – by Author Bob Chester
The Most Interesting Curves You've Never Heard Of by Robert G. Chester [caption id="attachment_13083" align="alignleft" width="340"] Author Robert G. Chester[/caption] Quick, what simple rotations simultaneously generate the circle, the parabola, and the intersection of a cylinder and a sphere? Can these rotations also subsume the hippopede of Eudoxus [1], the limaçon [2], Viviani’s curve [3], rhodonea [4], the lemniscate of Gerono [5], and Fuller’s “great circle railroad tracks of energy” [6]? Quasi-Spherical Orbits, or QSOs, are the dynamic three-dimensional curves that result when a point rotates simultaneously about two or more axes. These intriguing curves provide insights and yield results in mathematics and physics alike. Viviani's Curve [caption id="attachment_13087" align="alignleft" width="133"] Rotation a[/caption] A point rotates in the right hand direction around the z-axis. The orbit is a circle in…