  Explicit symplectic integrators have been important tools for accurate and
efficient approximations of mechanical systems with separable Hamiltonians. For
the first time, the article proposes for arbitrary Hamiltonians similar
integrators, which are explicit, of any even order, symplectic in an extended
phase space, and with pleasant long time properties. They are based on a
mechanical restraint that binds two copies of phase space together. Using
backward error analysis, KAM theory, and additional multiscale analysis, an
error bound of $\mathcal{O}(T\delta^l \omega)$ is established for integrable
systems, where $T$, $\delta$, $l$ and $\omega$ are respectively the (long)
simulation time, step size, integrator order, and some binding constant. For
non-integrable systems with positive Lyapunov exponents, such an error bound is
generally impossible, but satisfactory statistical behaviors were observed in a
numerical experiment with a nonlinear Schr\"{o}dinger equation.
