# Newton's graphical method as a canonical transformation

@article{Chin2018NewtonsGM, title={Newton's graphical method as a canonical transformation}, author={Siu A. Chin}, journal={arXiv: History and Philosophy of Physics}, year={2018} }

This work shows that, Newton's Proposition 1 in the {\it Principia}, is an {\it exact} graphical representation of a canonical transformation, a first-order symplectic integrator generated at a finite time-step by the Hamiltonian. A fundamental characteristic of this canonical transformation is to update the position and velocity vectors {\it sequentially}, thereby automatically conserving the phase-volume and the areal velocity due to a central force. As a consequence, the continuous force is… Expand

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