Olga Rossi

The relativistic mechanics in a nonholonomic setting: a unified approach to particles with non-zero mass and massless particles

A new approach to relativistic mechanics is proposed, suitable for describing in a unified way the dynamics of different kinds of relativistic particles. Mathematically, it is an application of a geometric theory of nonholonomic systems on fibred manifolds. We propose a setting based on a naturally constructed Lagrangian and a constraint on the 4-velocity of a particle that allows a unified approach to particles with any (positive/negative/zero) square of mass. The corresponding equations of motion are obtained and discussed. In particular, new forces are found (different from the usual Lorentz force type term), arising due to the nonholonomic constraint. A possible meaning and relation with forces previously proposed by Dicke is discussed. In particular, equations of motion of massless particles and of tachyons are studied and the corresponding dynamics are investigated.

Variational Sequences, Representation Sequences and Applications in Physics ?

Přehledový clanek obsahujici nove výsledky z oblasti variacnich posloupnosti konecneho řadu a jejich různe reprezentace, z důrazem na aplikace teorie variacnich symetrii a zakonů zachovani ve fyzice.

Homogeneous differential equations and the inverse problem of the calculus of variations

We study second order differential equations considering positive homogeneity of a general degree of the equations and of functions connected with them (like, for example, metrics or Lagrangians). Special attention is payed to semi-variational equations and to relationships between homogeneity properties and variationality (existence of local Lagrangians.