BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bernhard Maschke (U Claude Bernard Lyon 1Lyon) DTSTART:20240403T140000Z DTEND:20240403T150000Z DTSTAMP:20260423T023942Z UID:PHSeminar/3 DESCRIPTION:Title: The geometry of the state space of physical systems and the consequences on the definition of Port-Hamiltonian systems\nby Bernhard Maschke (U Claude Bernard Lyon 1Lyon) as part of Port-Hamiltonian Seminar\n\n\nAbstr act\nIn the first part\, we recall the geometric structure of the state sp ace of physical systems. Indeed\, for Thermodynamical systems\, it is well accepted that the system is first defined by its so-called equilibrium pr operties. These properties are defined by a set of relations among the ext ensive and intensive variables\, the Thermodynamic Phase variables\, which should satisfy the Gibbs' equations. Actually Gibbs' equations define a L egendre submanifold of the Thermodynamic Phase Space which is generated by a family of functions\, called thermodynamic functions. This Legendre sub manifolds actually defines the state space of the system.\n\nA similar con struction holds for Hamiltonian systems arising for mechanical systems or electro-mechanical systems' models\, when instead of defining a Hamiltonia n function\, one considers the reciprocal constitutive relations relating the energy and the co-energy variables. These reciprocal relations define a Lagrangian submanifold of the cotangent space of the energy variables (t he space of energy and the co-energy variables).\n\nIn the second part of the talk\, we shall draw the consequence of the definition of the state sp ace Lagrange or Legendre submanifolds for Hamiltonian and port Hamiltonian systems. Indeed\, defining the state space as a submanifold of some phase space\, corresponds to an implicit definition of the Hamiltonian dynamics . For irreversible Thermodynamic systems\, one defines a contact Hamiltoni an system on the Thermodynamic Phase Space\, leaving invariant some Legend re submanifold. For Hamiltonian systems defined on Lagrange submanifolds\, one defines a implicit Hamiltonian system restricted to some Lagrange sub manifold.\n\nWe shall finally present some ongoing work\, how this geometr ic perspective of the state space of physical systems\, leads to define a novel class of Port Hamiltonian systems equipped with a new type of port v ariables\, derived from the definition of Lagrange or Legendre submanifold s. We shall illustrate the work with various simple examples taken from ph ysical and engineering systems.\n LOCATION:https://researchseminars.org/talk/PHSeminar/3/ END:VEVENT END:VCALENDAR