Stabilization by manipulation of the Hamiltonian

Numerical integration of unstable differential equations should be avoided since a numerical error during thenth step produces erroneous initial values for the next step and thus deteriorates the subsequent integration in an unstable manner. A method is offered to stabilize the equations of motion corresponding to a given HamiltonianH by transformingH into a new HamiltonianH* which is equivalent to the Hamiltonian of a harmonic oscillator. In contrast to other methods of stabilization the realm of canonical mechanics is thus not abandoned. Perturbations are discussed and as examples the Keplerian motion and the motion of a gyroscope are presented.