  The Lyapunov exponents of a chaotic system quantify the exponential
divergence of initially nearby trajectories. For Hamiltonian systems the
exponents are related to the eigenvalues of a symplectic matrix. We make use of
this fact to develop a new method for the calculation of Lyapunov exponents of
such systems. Our approach avoids the renormalization and reorthogonalization
of usual techniques. It is also easily extendible to damped systems. We apply
our method to two examples of physical interest: a model system that describes
the beam halo in charged particle beams and the driven van der Pol oscillator.
