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.
Hickling, Fred; Davis, Wesley; and Woolverton, Heather
"Critical Energy of Torus Knots,"
Journal of the Arkansas Academy of Science: Vol. 49
, Article 15.
Available at: https://scholarworks.uark.edu/jaas/vol49/iss1/15