Anti-Newtonian dynamics
J. C. Sprott
Department of Physics,
University of
Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706
(Received 20 April 2009; accepted 2 June 2009)
ABSTRACT
This paper describes a world in which Newton’s first and second laws
hold, but Newton’s third law takes the form that the forces between
any
two objects are equal in magnitude and direction. The dynamics for
such
a system exhibit curious and unfamiliar features including chaos for
two bodies in two spatial dimensions.
Ref: J. C. Sprott,
Am. J. Phys.
77, 783-787 (2009)
The complete paper is available in
PDF
format.
See also animations
of these cases.
Return to Sprott's Books and Publications.
Fig. 1. Limit cycle of a rabbit and a fox in a one-dimensional
chase.
Fig. 2. Quasiperiodic trajectory of a rabbit and a fox in a
two-dimensional chase with no dissipation (animation).
Fig. 3. Quasiperiodic trajectory of a rabbit and a fox in a
two-dimensional chase with dissipation (animation).
Fig. 4. Chaotic trajectory of a rabbit and a fox in a
two-dimensional
chase with dissipation (animation).
Fig. 5. Chaotic trajectory of a rabbit being chased by two
identical
foxes with dissipation (animation).
