Semi-implicit Euler
A simple integrator that updates velocity first and then uses the new velocity for position — a small change that makes it far more stable than plain Euler.
Explicit (forward) Euler computes the change in position from the old velocity and the change in velocity from the old acceleration. It leaks energy: a spring or an orbit ramps up relentlessly and blows up. Semi-implicit Euler — also called symplectic Euler or Euler-Cromer — just swaps the order: update the velocity, then use that updated velocity for the position.
That single-line reordering makes the method symplectic: it conserves energy on average rather than drifting, so a spring system oscillates stably for hours. It is still only first-order accurate, but cheap and robust, which is why it is the default integrator in most game physics engines. For more precision you reach for Verlet or RK4. A fixed timestep is assumed — a varying dt breaks the stability.