Translating Souriau

This is the website for the reading group on Souriau's geometrical approach to mechanics, organised by Andrew Beckett within the Edinburgh Mathematical Physics Group.

In his influential book Structure of Dynamical Systems: a symplectic view of physics, written in 1970, Jean-Marie Souriau (1922-2012) introduced a geometrical formalism for mechanical systems based on symplectic geometry and the interplay between dynamics and symmetry. The book contains many interesting ideas, but is written in a somewhat idiosyncratic language which is often at odds with modern usage. The purpose of the reading group is to understand Souriau's ideas and at the same translate them to a more standard mathematical language.

We intend to meet every other Friday in JCMB from 10:30-12:30, followed by lunch, starting on 4 March.

Meeting schedule

  1. Friday, 4 March 2022, 10:30-12:30
    JCMB 5328
    The geometric structure of classical mechanics (I)
    Andrew Beckett
    We start with Section 12 in the book.
  2. Friday, 18 March 2022, 10:30-12:30
    JCMB 5328
    The geometric structure of classical mechanics (II)
    Andrew Beckett
    We continue with Section 12 in the book.
  3. Friday, 1 April 2022, 10:30-12:30
    JCMB 6201
    The geometric structure of classical mechanics (III)
    Andrew Beckett
    We continue with Section 12 in the book.
  4. Thursday, 14 April 2022, 10:30-12:30
    JCMB 6201
    Dynamical groups
    José Figueroa-O'Farrill
    A sort of review and basic notions of dynamical groups
  5. Friday, 22 April 2022, 10:30-12:30
    JCMB 6201
    Galilean relativity
    José Figueroa-O'Farrill
    More on Section 12 and some bits of Section 11 as needed.
  6. Friday, 6 May 2022, 10:30-12:30
    JCMB 6201
    The principles of symplectic mechanics
    José Figueroa-O'Farrill
    Section 13, hopefully.
  7. Friday, 27 May 2022, 10:30-12:30
    JCMB 6201
    Elementary relativistic systems and coadjoint orbits of Poincaré
    José Figueroa-O'Farrill
    First half of Section 14. (Alas the recording did not work... only sound.)

References

a.d.k.beckett at ed.ac.uk