INMABB   05456
INSTITUTO DE MATEMATICA BAHIA BLANCA
Unidad Ejecutora - UE
artículos
Título:
GENERALIZED NONHOLONOMIC MECHANICS, SERVOMECHANISMS AND RELATED BRACKETS
Autor/es:
H. CENDRA; S. GRILLO
Revista:
JOURNAL OF MATHEMATICAL PHYSICS
Editorial:
Amer. Inst. Phys.
Referencias:
Lugar: Huntington Quadrangle Melville NY; Año: 2006 vol. 47 p. 1 - 29
ISSN:
0022-2488
Resumen:
It is well-known that nonholonomic systems obeying D´Alembert´s principle are described on the Hamiltonian side, after using the Legendre transformation, by the so called almost-Poisson brackets. In this paper we define the Lagrangian and Hamiltonian sides of a class of generalized nonholonomicsystems (GNHS), obeying a generalized version of D´Alembert´s principle, such as rubber wheels (like some simplified models of pneumatic tires) and certain servomechanisms (like the controlled inverted pendulum), and show that corresponding equations of motion can also be described in terms of a bracket. We present emph{essentially all} possible brackets in terms of which the mentioned equations can be written down, which include the brackets that appear in the literature, and point out those (if any) that are naturally related to each system. In particular, we show there always exists a Leibniz bracket related to a GNHS, and conversely, that every Leibniz system is a GNHS. The control of the inverted pendulum on a cart is studied as an illustrative example.