Physics
Elastic rods
Bending and twisting: cables, hair, DNA supercoiling.
What happens
A flexible rod living in three dimensions: a cable sags into a catenary between two posts, a clamped cantilever is checked live against the textbook qL⁴/8EI, a whip cracks on its handle. The tube's colour rides the local curvature - straight runs stay cool, tight bends glow warm. Grab any point with the mouse and pull, or pluck it upward or sideways and watch the wave travel in space. The bending slider spans cooked spaghetti to spring steel; the damping slider decides how long the ringing lives.
Equations used in the module
Equations E_bend = ½ EI ∫κ² ds δ = qL⁴/(8EI) + PL³/(3EI) y(s) = −qs²(6L²−4Ls+s²)/(24EI) − Ps²(3L−s)/(6EI) y = y₀ − a[cosh((x−x_c)/a)−cosh(L/(2a))] 2a sinh(L/(2a)) = l
