Abstract
Most elementary numerical schemes found useful for solving classical
trajectory problems are canonical transformations. This fact should be
make more widely known among teachers of computational physics and Hamiltonian
mechanics. It is very surprising that in order to solve a simple second-order
differential equation, one has to invoke the deepest part, the Poissonian
formulation, of classical mechanics. From the perspective of advanced
mechanics, there are no bewildering number of seemingly arbitrary elementary
schemes based on Taylor's expansion. There are only two canonical
second-order algorithms, on the basis of which one can build numerical schemes
of any order.
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