35 citations · 76 across the 10 of their papers we have counts for
12 papers
On Gibbs states of mechanical systems with symmetries
Charles-Michel Marle
Gibbs states for the Hamiltonian action of a Lie group on a symplectic manifold were studied, and their possible applications in Physics and Cosmology were considered, by the Frenc…
The works of William Rowan Hamilton in geometrical optics and the Malus-Dupin theorem
Charles-Michel Marle
The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on tw…
From tools in symplectic and Poisson geometry to Souriau's theories of statistical mechanics and thermodynamics
Charles-Michel Marle
I present in this paper some tools in Symplectic and Poisson Geometry in view of their applications in Geometric mechanics and Mathematical Physics. After a short discussion of the…
A direct proof of Malus' theorem using the symplectic structure of the set of oriented straight lines
Charles-Michel Marle
We present a direct proof of Malus' theorem in geometrical Optics founded on the symplectic structure of the set of all oriented straight lines in an Euclidean affine space. Nous p…
Relativity, the Special Theory, explained to Children (from 7 to 107 years old)
Charles-Michel Marle
The author thinks that the main ideas or Relativity Theory can be explained to children (around the age of 15 or 16) without complicated calculations, by using very simple argument…
Lie, symplectic and Poisson groupoids and their Lie algebroids
Charles-Michel Marle
Groupoids are mathematical structures able to describe symmetry properties more general than those described by groups. They were introduced (and named) by H. Brandt in 1926. Aroun…