  We develop continuous-stage Runge-Kutta-Nystr\"Om (csRKN) methods in this
paper. By leading weight function into the formalism of csRKN methods and
modifying the original pattern of continuous-stage methods, we establish a new
and larger framework for csRKN methods and it enables us to derive more
effective RKN-type methods. Particularly, a variety of classical weighted
orthogonal polynomials can be used in the construction of RKN-type methods. As
an important application, new families of symmetric and symplectic integrators
can be easily acquired in such framework. Numerical experiments have verified
the effectiveness of the new integrators presented in this paper.
