“…2.3 and 3.5 for a precise definition of continuous and discrete symplecticity. Examples of Hamiltonian systems appearing in science and engineering include but are not limited to the structural biology (Gay-Balmaz et al 2009), molecular dynamics (Stavros 2014;Manning and Maddocks 1999), mathematical models in ecosystem dynamics (Kirwan 2008), superconductivity (Bogolyubov 1972), plasma physics (Larsson 1996), celestial mechanics and cosmology (Arnold et al 2006), fluid mechanics (Desbrun et al 2014;Gawlik et al 2011), mechanics of materials and structures , theoretical physics (Esposito et al 2004;Marsden 1988), aerospace engineering (Kasdin et al 2005), satellite dynamics and control (Kuang et al 2003;Koon et al 2011), kinematics and dynamics of mechanisms and robots (Macchelli et al 2009;Chen 1990) and other areas of seismic (Luo et al 2013), mechanical and electrical (Clemente-Gallardo and Scherpen 2003) engineering. Symplectic integrators are methods specially formulated to produce a symplectic flows on the phase space.…”