SIGMA 3 (2007), 036, 33 pages math.DS/0703043
Contribution to the Vadim Kuznetsov Memorial Issue
A 'User-Friendly' Approach to the Dynamical Equations of Non-Holonomic Systems
Department of Mathematics, University of Turin, Italy
Received November 29, 2006, in final form February 13, 2007; Published online March 01, 2007
Two effective methods for writing the dynamical
equations for non-holonomic systems are illustrated. They are
based on the two types of representation of the constraints: by
parametric equations or by implicit equations. They can be applied
to linear as well as to non-linear constraints. Only the basic
notions of vector calculus on Euclidean 3-space and on tangent
bundles are needed. Elementary examples are illustrated.
non-holonomic systems; dynamical systems.
pdf (457 kb)
ps (414 kb)
tex (278 kb)
- Benenti S., Geometrical aspects of the dynamics of non-holonomic
systems, Rend. Sem. Mat. Univ. Pol. Torino 54
- Bullo F., Lewis A.D., Geometric control of mechanical systems,
Texts in Applied Mathematics, Vol. 49, Springer, Berlin,
- Carathéodory C.,
Sur les équations de la mécanique,
Actes Congrès Interbalcanian Math. (1934, Athènes),
- Cortés Monforte J., Geometrical, control and numerical aspects
of nonholonomic systems, Lecture Notes in Mathematics,
Vol. 1793, Springer, Berlin, 2002.
- Gantmacher F., Lectures in analytical mechanics, Mir, Moscow,
- Marle C.-M., Reduction of constrained mechanical systems and
stability of relative equilibria, Comm. Math. Phys.
174 (1995), 295-318.
- Massa E., Pagani E., A new look at classical mechanics of
constrained systems, Ann. Inst. H. Poincaré Phys. Théor.
66 (1997), 1-36.
- Massa E., Pagani E., Classical dynamics of non-holonomic systems:
a geometric approach, Ann. Inst. H. Poincaré Phys.
Théor. 55 (1991), 511-544.
- Neimark J.I., Fufaev N.A., Dynamics of nonholonomic systems,
Translations of Mathematical Monographs, Vol. 33, American
Mathematical Society, Providence, Rhode Island, 1972.
- Oliva W.M., Kobayashi M.H., A note on the conservation of energy
and volume in the setting of nonholonomic mechanical systems,
Qual. Theory Dyn. Syst. 4 (2004),