Newton's graphical method for central force orbits.

In the Principia, Book 1, Proposition 1, Newton gave a geometrical proof of angular momentum conservation for central forces. A geometrical construction associated with this proof provides a very efficient graphical method to obtain approximate orbital curves for such forces that can be traced with a ruler and a pencil. Newton's geometrical construction also satisfies a discrete form of energy conservation and it is time reversal invariant. An algorithm corresponding to this construction provides an efficient and stable numerical method to integrate the equations of motion of classical mechanics. In the past, this algorithm has been rediscovered several times without recognizing its connection to Newton's geometrical construction. [ABSTRACT FROM AUTHOR]