Corpus ID: 53709794

Newton's graphical method as a canonical transformation

  title={Newton's graphical method as a canonical transformation},
  author={Siu A. Chin},
  journal={arXiv: History and Philosophy of Physics},
  • S. Chin
  • Published 11 October 2018
  • Physics
  • arXiv: History and Philosophy of Physics
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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