Live, browser-based visualisations of elliptic integrals and functions. All computations run client-side. Built with Three.js, D3, and KaTeX.
Celestial mechanics & orbital dynamics
Jacobi elliptic functions
Nonlinear dynamics · Jacobi sn/cn/dn
Exact period for large-amplitude oscillations via $K(k^2)$, live pendulum animation using $\mathrm{sn}(t|m)$, phase-portrait with separatrix, and period divergence as $\theta_0 \to \pi$. Extends to compound pendula.
Rigid body rotation coming soon
Torque-free rotation of an asymmetric top: $\omega_1 = \omega_0\,\mathrm{cn}(t|m)$, polhode animation, and Euler angle integration.
Nonlinear waves & signal processing
KdV equation coming soon
Exact KdV cnoidal wave solution $u(x,t) = A\,\mathrm{cn}^2(\kappa(x-vt)|m)$ animated across the soliton limit $m \to 1$.
Weierstrass & modular forms
Complex analysis coming soon
Domain-colouring of $\wp(z)$ over the complex plane, lattice geometry from invariants $g_2, g_3$, and the group law on $y^2 = 4x^3 - g_2 x - g_3$.