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.
