The equations of motion of a nonrelativistic particle in an attractive 1/r central force are developed, and integrated by a digital computer. The results are presented graphically, and representative orbits are sketched.

1.
After completion of this work, our attention was called to an unpublished study of this problem: W. E. Waters, “Motion of Electrons between Concentric Cylinders,” Diamond Ordnance Fuze Laboratories Technical Report No. 525 (November 1957). Waters discusses the problem in detail and has determined the shape and time‐development of a number of orbits by means of an analog computer.
2.
R. G.
Herb
,
T.
Pauly
, and
K. J.
Fisher
,
Bull. Am. Phys. Soc.
8
,
336
(
1963
).
Google Scholar
 
3.
In this paper we are concerned only with motion in a plane perpendicular to the axis of symmetry of the field. If the particle has a component of velocity along this axis (which, in fact, is necessary for the operation of the Orbitron), the longitudinal and transverse motions are easily separated; and the transverse component of the motion is described here.
4.
For some purposes it is convenient to express the relations derived here in terms of sinψ instead of L, by making the substitution
L = (2mK0)12r0sinψ
. This simplifies especially Eqs. (1) through (5) and (7), and the definitions of u and β.
This content is only available via PDF.
© 1963 The American Institute of Physics.
1963
The American Institute of Physics
You do not currently have access to this content.