◆ frontier30 mindraft

Discretising the action instead of the equations

Variational integrators derive the update from a discrete least-action principle. Symplecticity and conserved momenta then follow automatically rather than being imposed.

assumes you already have

Why a worse method gives a better orbit

Planned outline

The continuous action, and least action as the source of the equations of motion.
A discrete Lagrangian, and the discrete Euler-Lagrange equations.
Recovering velocity Verlet from a midpoint discrete Lagrangian - it was variational all along.
The discrete Noether theorem: conserved momenta to machine precision, not to O(h^p).
Where this beats symplectic-by-construction: constraints, contact, non-smooth mechanics.

Interactives planned

Each numbered point above gets at least one thing you can manipulate, not a figure. See AGENTS.md for the widget vocabulary and the rule that every lesson ships at least one graded interaction and one recall card.