In textbooks and lectures on mechanics, after Newton's equations of motion it is usual to consider the Lagrange equations and thereafter Hamilton's equations. One first of all gets the impression that with the constant introduction of new equations, mechanics is not becoming simpler but more complicated. Only by an attempt to solve a non-trivial problem of particle mechanics - such as some form of 3-body problem in gravitational fields - does one come to realize that Hamilton's equations are helpful.