Editing Hamiltonian system (section)

===Example===
{{main|Simple harmonic motion}}

An example of a time-independent Hamiltonian system is the harmonic oscillator. Consider the system defined by the coordinates <math>\boldsymbol{p} = m\dot{x}</math> and <math>\boldsymbol{q} = x</math>. Then the Hamiltonian is given by

: <math> H = \frac{p^2}{2m} + \frac{kq^2}{2}.</math>

The Hamiltonian of this system does not depend on time and thus the energy of the system is conserved.