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In this paper we develop a straightforward procedure to construct higherdimensional isochronous Hamiltonian systems. We first show that a class ofsingular Hamiltonian systems obtained through the $\Omega$-modified procedureis equivalent to constrained Newtonian systems. Even though such systems admitisochronous oscillations, they are effectively one degree of freedom systemsdue to the constraints. Then we generalize the procedure in terms of$\Omega_i$-modified Hamiltonians and identify suitable canonically conjugatecoordinates such that the constructed $\Omega_i$-modified Hamiltonian is\emph{nonsingular} and the corresponding Newton's equation of motion isconstraint free. The procedure is first illustrated for two dimensional systemsand subsequently extended to $N$-dimensional systems. The general solution ofthese systems are obtained by integrating the underlying equations and is shownto admit isochronous as well as amplitude independent quasiperiodic solutionsdepending on the choice of parameters.

Method of generating $N$-dimensional isochronous nonsingular Hamiltonian systems