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SUMMARY:Bernhard Maschke (U Claude Bernard Lyon 1Lyon)
DTSTART:20240403T140000Z
DTEND:20240403T150000Z
DTSTAMP:20260513T222341Z
UID:PHSeminar/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PHSeminar/3/
 ">The geometry of the state space of physical systems and the consequences
  on the definition of Port-Hamiltonian systems</a>\nby Bernhard Maschke (U
  Claude Bernard Lyon 1Lyon) as part of Port-Hamiltonian Seminar (pH Semina
 r)\n\n\nAbstract\nIn the first part\, we recall the geometric structure of
  the state space of physical systems. Indeed\, for Thermodynamical systems
 \, it is well accepted that the system is first defined by its so-called e
 quilibrium properties. These properties are defined by a set of relations 
 among the extensive and intensive variables\, the Thermodynamic Phase vari
 ables\, which should satisfy the Gibbs' equations. Actually Gibbs' equatio
 ns define a Legendre submanifold of the Thermodynamic Phase Space which is
  generated by a family of functions\, called thermodynamic functions. This
  Legendre submanifolds actually defines the state space of the system.\n\n
 A similar construction holds for Hamiltonian systems arising for mechanica
 l systems or electro-mechanical systems' models\, when instead of defining
  a Hamiltonian function\, one considers the reciprocal constitutive relati
 ons relating the energy and the co-energy variables. These reciprocal rela
 tions define a Lagrangian submanifold of the cotangent space of the energy
  variables (the space of energy and the co-energy variables).\n\nIn the se
 cond part of the talk\, we shall draw the consequence of the definition of
  the state space Lagrange or Legendre submanifolds for Hamiltonian and por
 t Hamiltonian systems. Indeed\, defining the state space as a submanifold 
 of some phase space\, corresponds to an implicit definition of the Hamilto
 nian dynamics. For irreversible Thermodynamic systems\, one defines a cont
 act Hamiltonian system on the Thermodynamic Phase Space\, leaving invarian
 t some Legendre submanifold. For Hamiltonian systems defined on Lagrange s
 ubmanifolds\, one defines a implicit Hamiltonian system restricted to some
  Lagrange submanifold.\n\nWe shall finally present some ongoing work\, how
  this geometric perspective of the state space of physical systems\, leads
  to define a novel class of Port Hamiltonian systems equipped with a new t
 ype of port variables\, derived from the definition of Lagrange or Legendr
 e submanifolds. We shall illustrate the work with various simple examples 
 taken from physical and engineering systems.\n
LOCATION:https://researchseminars.org/talk/PHSeminar/3/
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