Geodesic
A “User-Friendly” Approach to the Dynamical Equations of Non-Holonomic Systems
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: non-holonomic systems; dynamical systems. 
@article{SIGMA_2007_3_a35,
     author = {Sergio Benenti},
     title = {A~{\textquotedblleft}User-Friendly{\textquotedblright} {Approach} to the {Dynamical} {Equations} of {Non-Holonomic} {Systems}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a35/}
}
TY  - JOUR
AU  - Sergio Benenti
TI  - A “User-Friendly” Approach to the Dynamical Equations of Non-Holonomic Systems
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a35/
LA  - en
ID  - SIGMA_2007_3_a35
ER  - 
%0 Journal Article
%A Sergio Benenti
%T A “User-Friendly” Approach to the Dynamical Equations of Non-Holonomic Systems
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a35/
%G en
%F SIGMA_2007_3_a35
Sergio Benenti. A “User-Friendly” Approach to the Dynamical Equations of Non-Holonomic Systems. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a35/

[1] Benenti S., “Geometrical aspects of the dynamics of non-holonomic systems”, Rend. Sem. Mat. Univ. Pol. Torino, 54 (1996), 203–212 | MR | Zbl

[2] Bullo F., Lewis A. D., Geometric control of mechanical systems, Texts in Applied Mathematics, 49, Springer, Berlin, 2004 | MR

[3] Carathéodory C., “Sur les équations de la mécanique”, Actes Congrès Interbalcanian Math. (1934, Athènes), 1935, 211–214

[4] Cortés Monforte J., Geometrical, control and numerical aspects of nonholonomic systems, Lecture Notes in Mathematics, 1793, Springer, Berlin, 2002 | MR | Zbl

[5] Gantmacher F., Lectures in analytical mechanics, Mir, Moscow, 1970

[6] Marle C.-M., “Reduction of constrained mechanical systems and stability of relative equilibria”, Comm. Math. Phys., 174 (1995), 295–318 | DOI | MR | Zbl

[7] Massa E., Pagani E., “A new look at classical mechanics of constrained systems”, Ann. Inst. H. Poincaré Phys. Théor., 66 (1997), 1–36 | MR | Zbl

[8] Massa E., Pagani E., “Classical dynamics of non-holonomic systems: a geometric approach”, Ann. Inst. H. Poincaré Phys. Théor., 55 (1991), 511–544 | MR | Zbl

[9] Neimark J. I., Fufaev N. A., Dynamics of nonholonomic systems, Translations of Mathematical Monographs, 33, American Mathematical Society, Providence, Rhode Island, 1972 | Zbl

[10] 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), 383–411 | DOI | MR