Dynamics of the Hamiltonian H(x,y) $=$ \textbar x\textbar $+$\textbar y\textbar

We investigate the classical dynamics of the Hamiltonian (1) $H(x,y)=\;\vert x\vert +\vert y\vert $, and normalize the energy value to be H(x,y) $=$ 1. The equations of motion are (2) $\frac{dx}{dt}=\frac{\partial H}{\partial y}=sgn(y),\quad \quad \frac{dy}{dt}=-\frac{\partial H}{\partial x}=-sgn(x).$ In addition to proving all solutions are periodic, we also calculate explicitly the exact analytical solutions to Eq. (2). Further, we show that x(t) and y(t) have many features in common with the standard trigonometric cosine and sine functions. The work is based on the previous results of Mickens [1]. \underline {Reference} [1] R.E. Mickens, ``Some properties of square (periodic) functions''. Proceedings of Dynamic Systems and Applications 7 (2016), 282-286.