Calculate the curvature and torsion for the following trajectories given by x(t) x(t) x + y(t)ý + z(t) 2. Sketch each trajectory. (a) (b) (c) x(t) = Rsin(wt), y(t): = where R and we are constant. Rcos(wt), z(t) = 0, x(t) = Rsin(wt), y(t) = Rcos(wt), z(t) = vat, where R, w, and va are constant. = x(t) = R₁ sin(wt), y(t) = R₂ cos(wt), z(t) = 0, where R₁, R₂, and we are constant. Then set R₁ = 1, R₂ = 2, and w = 1 and plot k(t) for 0 ≤ t ≤ 2π.
Calculate the curvature and torsion for the following trajectories given by x(t) x(t) x + y(t)ý + z(t) 2. Sketch each trajectory. (a) (b) (c) x(t) = Rsin(wt), y(t): = where R and we are constant. Rcos(wt), z(t) = 0, x(t) = Rsin(wt), y(t) = Rcos(wt), z(t) = vat, where R, w, and va are constant. = x(t) = R₁ sin(wt), y(t) = R₂ cos(wt), z(t) = 0, where R₁, R₂, and we are constant. Then set R₁ = 1, R₂ = 2, and w = 1 and plot k(t) for 0 ≤ t ≤ 2π.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
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