Atomic, Molecular and Optical Physics Commons^™

Critical Energy Of Torus Knots, Fred Hickling, Wesley Davis, Heather Woolverton

Journal of the Arkansas Academy of Science

The energy of a smoothly parameterized knot y(t) is defined as rr\ i i lp7 \\dn dsdt Jo Jo \||7M-7(0f (D(t(s),T(t))) 2 j\\ds \\dt where D(y (s), y(t)) is the arc length between the two points y (s) and y(t) on the curve. Simple calculus based arguments are used to locate critical values of the energy functional for torus knots. Explicitly the curves given parametrically by °(«*)W = (V2°iSri).JSSBe V2 C s7nS are CriticalP ° intS ° fthe energy functional whenever a and b are relatively prime.