A unified approach to constrained mechanical systems as implicit differential equations

F. Barone; R. Grassini; G. Mendella

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 70, Issue: 6, page 515-546
  • ISSN: 0246-0211

How to cite

top

Barone, F., Grassini, R., and Mendella, G.. "A unified approach to constrained mechanical systems as implicit differential equations." Annales de l'I.H.P. Physique théorique 70.6 (1999): 515-546. <http://eudml.org/doc/76829>.

@article{Barone1999,
author = {Barone, F., Grassini, R., Mendella, G.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {constrained mechanics; global time-independent Lagrangian dynamics; nonconservative forces; nonholonomic constraints; implicit differential equations; cotangent space; configuration space; 1-forms},
language = {eng},
number = {6},
pages = {515-546},
publisher = {Gauthier-Villars},
title = {A unified approach to constrained mechanical systems as implicit differential equations},
url = {http://eudml.org/doc/76829},
volume = {70},
year = {1999},
}

TY - JOUR
AU - Barone, F.
AU - Grassini, R.
AU - Mendella, G.
TI - A unified approach to constrained mechanical systems as implicit differential equations
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 70
IS - 6
SP - 515
EP - 546
LA - eng
KW - constrained mechanics; global time-independent Lagrangian dynamics; nonconservative forces; nonholonomic constraints; implicit differential equations; cotangent space; configuration space; 1-forms
UR - http://eudml.org/doc/76829
ER -

References

top
  1. [1] V.I. Arnold, V.V. Kozlov and A.I. Neishtadt, Dynamical Systems III, Springer, New York, 1988. MR923953
  2. [2] F. Barone and R. Grassini, On the second-order Euler-Lagrange equation in implicit form, Ric. Mat.46 (1) (1997) 221-233. Zbl0948.70523MR1615750
  3. [3] F. Barone, R. Grassini and G. Mendella, A generalized Lagrange equation in implicit form for nonconservative mechanics, J. Phys. A: Math. Gen.30 (1997) 1575-1590. Zbl1001.37503MR1449998
  4. [4] J.F. Cariñena and M.F. Rañada, Lagrangian systems with constraints: a geometric approach to the method of Lagrange multipliers, J. Phys. A: Math. Gen.26 (1993) 1335-1351. Zbl0772.58016MR1212006
  5. [5] M. Crampin, Tangent bundle geometry for Lagrangian dynamics, J. Phys. A: Math. Gen.16 (1983) 3755-3772. Zbl0536.58004MR727054
  6. [6] P. Dazord, Mécanique Hamiltonienne en présence de contraintes, Ill. J. Math.38 (1994) 148-175. Zbl0790.58018MR1245839
  7. [7] M. De Léon and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, North-Holland, Amsterdam, 1989. Zbl0687.53001MR1021489
  8. [8] M. De Léon and D.M. De Diego, On the geometry of non-holonomic Lagrangian systems, J. Math. Phys.37 (7) (1996) 3389-3414. Zbl0869.70008MR1401231
  9. [9] M. De Léon and D.M. De Diego, Mechanical systems with non-linear constraints, Preprint. Zbl0874.70012
  10. [10] C. Godbillon, Géométrie Differentielle et Mécanique Analytique, Hermann, Paris, 1969. Zbl0174.24602MR242081
  11. [11] M.J. Gotay and J. Nester, Presymplectic Lagrangian systems I: The constraint algorithm and the equivalence theorem, Ann. Inst. Henri Poincaré30 (2) (1979) 129-142. Zbl0414.58015MR535369
  12. [12] M.J. Gotay and J. Nester, Presymplectic Lagrangian systems II: The second-order equation problem, Ann. Inst. Henri Poincaré32 (1) (1980) 1-13. Zbl0453.58016MR574809
  13. [13] X. Grácia and J.M. Pons, Constrained systems: A unified geometric approach, Int. J. Th. Phys.30 (4) (1991) 511-516. Zbl0733.58014MR1102803
  14. [14] X. Grácia and J.M. Pons, A generalized geometric framework for constrained systems, Diff. Geom. Appl.2 (1992) 223-247. Zbl0763.34001MR1245325
  15. [15] C.M. Marle, Reduction of constrained mechanical systems and stability of relative equilibria, Comm. Math. Phys.74 (1995) 295-318. Zbl0859.70012MR1362167
  16. [16] G. Marmo, G. Mendella and W.M. Tulczyjew, Symmetries and constants of the motion for dynamics in implicit form, Ann. Inst. H. Poincaré57 (2) (1992) 147-166. Zbl0766.58020MR1184887
  17. [17] G. Marmo, G. Mendella and W.M. Tulczyjew, Constrained Hamiltonian systems as implicit differential equations, J. Phys. A: Math. Gen.30 (1997) 277- 293. Zbl0922.58025MR1447117
  18. [18] W.M. Tulczyjew, Geometric Formulations of Physical Theories, Bibliopolis, Napoli, 1989. Zbl0707.58001MR1026453
  19. [19] A.M. Vershik and L.D. Fadeev, Differential geometry and Lagrangian mechanics with constraints, Soviet Physics-Doklady17 (1) (1972) 34-36. Zbl0243.70014
  20. [20] A.M. Vershik and L.D. Fadeev, Lagrangian mechanics in invariant form, Sel. Math. Sov.1 (1975) 339-350. Zbl0518.58015
  21. [21] E.T. Whittaker, A Treatise on the Analitical Dynamics of Particles and Rigid Bodies, Cambridge University Press, 1927. MR992404JFM53.0732.02
  22. [22] N. Woodhouse, Geometric Quantization, Clarendon Press, Oxford, 1980. Zbl0458.58003MR605306

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.