Vol.5, No 1, 2006 pp. 1-24
UDC 531.01
Invited Paper

THE LAGRANGIAN GEOMETRICAL MODEL
AND THE ASSOCIATED DYNAMICAL SYSTEM
OF A NONHOLONOMIC MECHANICAL SYSTEM
Radu Miron1, Valer Nimineţ2
1Department of Geometry, Faculty of Mathematics
"Al.I.Cuza" University, 700506 – Iaşi, România
e-mail: radu.miron@uaic.ro
2Department of Geometry, Faculty of Sciences University of Bacău, Romania
e-mail: valern@ub.ro

Abstract. One considers a Lagrangian nonholonomic mechanical system ? =  , with  , whose  evolution equations are (1.3). One associates to system ? a canonical semispray S?  on the phase space TM, which has the integral curves given by the evolution equations of ?. The Lagrange geometry of system ? is the geometry of semispray S? which is a dynamical system, on TM, intrinsically associated to ?. The obtained results are  new and original.
Key words: Lagrange spaces, Semispray, Dynamical System, Lagrangian mechanical systems

GEOMETRIJSKI MODEL LAGRANŽIJANA I PRIDRUŽENI  DINAMIČKI SISTEM 
NEHOLONOMNOG MEHANIČKOG SISTEMA
Razmatra se geometrijski model Lagranžiana i pridruženi dinamički sistem mehaničkog sistema   , sa  , čije su evolucione jednačine (1.3). Kanonski semisprej S? udružuje se u system  ?  na prostoru faze TM, koja ima integralne krive date evolucionim jednačinama ?. Lagranžeova geometrija sistema ? je geometrija S? koja je dinamički system, na TM, suštinski pridružen u ?. Dobijeni rezultati su novi  i originalni.
Ključne reči: Lagranžeov prostor, semisprej, dinamički sistem, Lagranžijan mehaničkog sistema.