  We develop continuous-stage Runge-Kutta-Nystr\"{o}m (csRKN) methods for
solving second order ordinary differential equations (ODEs) in this paper. The
second order ODEs are commonly encountered in various fields and some of them
can be reduced to the first order ODEs with the form of separable Hamiltonian
systems. The symplecticity-preserving numerical algorithm is of interest for
solving such special systems. We present a sufficient condition for a csRKN
method to be symplecticity-preserving, and by using Legendre polynomial
expansion we show a simple way to construct such symplectic RKN type method.
