This Letter focuses on form invariance and Noether symmetries of mechanico-electrical systems. Based on the invariance of Hamiltonian actions for mechanico-electrical systems under the infinitesimal transformation of the coordinates, the electric quantities and the time, the authors present the Noether symmetry transformation, the Noether quasi-symmetry transformation, the generalized Noether q...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...

Different deformations of the Poincaré symmetries have been identified for various non-commutative spaces (e.g. κ-Minkowski, sl(2, R), Moyal). We present here the deformation of the Poincaré symmetries related to Snyder space-time. The notions of smooth “K-loop”, a non-associative generalization of Abelian Lie groups, and its infinitesimal counterpart given by the Lie triple system are the key ...

We study the additional symmetries associated with the q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries, the q-KP hierarchy can be consistently reduced to the so-called q-deformed constrained KP (q-cKP) hierarchy. We then show that the additional symmetries acting on the wave function can be viewed as infi...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...

We address the problem of characterisation null-forms conic 3-dimensional systems, that is, control-affine systems whose field admissible velocities forms a (without parameters) in tangent space. Those have been previously identified as simplest control under nonholonomic constraint or zero curvature. In this work, we propose direct among all by studying Lie algebra infinitesimal symmetries. Na...

We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of arbitrary-dimensional bar-joint frameworks with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on grouplabeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks wh...

In the framework of covariant classical mechanics (i.e. , generally relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of geometric objects. We show that the (holonomic) infinitesimal symmetries of the cosymplectic structure and of its horizontal potentials are also symmetries of spacel...