We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton’s law with the simplest measurement theory leads to Lagrangian mechanics, while use of conformal m...

The Ward identities for amplitudes at the tree level are derived from symmetries of the corresponding classical dynamical systems. The result are aplied to some 2 → n amplitudes supported by the Lódź University grant No. 269. supported by KBN grant No. 5 P03B 060 21 1 I Introducion Threshold amplitudes provide one of the rare examples of problems in quantum field theory which are both interesti...

different symmetries play a role in understanding the meaning of a sentence. syntacticians have been aware of this issue and have used a variety of symmetries in their analyses. when the arabic syntax became familiar with the aristotelian logic and received some philosophical issues, most of the syntacticians focused upon the arabic symmetry and few attentions were directed towards other symmet...

Adiscrete version of Lagrangian reduction is developed within the context of discrete time Lagrangian systems on G G, where G is a Lie group. We consider the case when the Lagrange function is invariantwith respect to the action ofan isotropysubgroup ofa¢xed element in the representation space of G. Within this context, the reduction of the discrete Euler^Lagrange equations is shown to lead to ...

This paper is devoted to the study of mechanical systems subjected external forces in framework symplectic geometry. We obtain Noether’s theorem for Lagrangian with forces, among other results regarding symmetries and conserved quantities. particularize our so-called Rayleigh dissipation, i.e., that are derived from a dissipation function, illustrate them some examples. Moreover, we present the...

This paper addresses the optimal control and selection of gaits in a class of nonholonomic locomotion systems that exhibit group symmetries. We study optimal gaits for the snakeboard, a representative example of this class of systems. We employ Lagrangian reduction techniques to simplify the optimal control problem and describe a general framework and an algorithm to obtain numerical solutions ...

This paper addresses the optimal control and selection of gaits in a class of nonholonomic locomotion systems that exhibit group symmetries. We study optimal gaits for the snakeboard, a representative example of this class of systems. We employ Lagrangian reduction techniques to simplify the optimal control problem and describe a general framework and an algorithm to obtain numerical solutions ...