On D’Alembert’s Principle

Larry M. Bates; James M. Nester

Communications in Mathematics (2011)

  • Volume: 19, Issue: 1, page 57-72
  • ISSN: 1804-1388

Abstract

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A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.

How to cite

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Bates, Larry M., and Nester, James M.. "On D’Alembert’s Principle." Communications in Mathematics 19.1 (2011): 57-72. <http://eudml.org/doc/196679>.

@article{Bates2011,
abstract = {A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.},
author = {Bates, Larry M., Nester, James M.},
journal = {Communications in Mathematics},
keywords = {nonholonomic constraints; d’Alembert’s principle; nonholonomic constraints; d'Alembert's principle},
language = {eng},
number = {1},
pages = {57-72},
publisher = {University of Ostrava},
title = {On D’Alembert’s Principle},
url = {http://eudml.org/doc/196679},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Bates, Larry M.
AU - Nester, James M.
TI - On D’Alembert’s Principle
JO - Communications in Mathematics
PY - 2011
PB - University of Ostrava
VL - 19
IS - 1
SP - 57
EP - 72
AB - A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.
LA - eng
KW - nonholonomic constraints; d’Alembert’s principle; nonholonomic constraints; d'Alembert's principle
UR - http://eudml.org/doc/196679
ER -

References

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  2. Bates, L., Śniatycki, J., 10.1016/0034-4877(93)90073-N, Reports on Mathematical Physics 32 1993 99–115 (1993) MR1247165DOI10.1016/0034-4877(93)90073-N
  3. Cantrijn, F., de León, M., Marrero, J., de Diego, D., 10.1063/1.532686, Journal of mathematical physics 40 1999 795–820 (1999) MR1674283DOI10.1063/1.532686
  4. Cushman, R., Kempainen, D., Śniatycki, J., A classical particle with spin realized by reduction of a nonlinear nonholonomic constraint, Reports on mathematical physics 41 (1) 1998 133–142 (1998) MR1617882
  5. de León, M., de Diego, D., 10.1007/BF02435796, International journal of theoretical physics 36 (4) 1997 979–995 (1997) MR1445410DOI10.1007/BF02435796
  6. Giaquinta, M., Hildebrandt, S., Calculus of Variations I, Number 310 in Grundlehren der mathematischen Wissenschaften. Springer-Verlag 1996 (1996) MR1368401
  7. Goldstein, H., Poole, C., Safko, J., Classical mechanics, Addison-Wesley, third edition 2002 (2002) MR0043608
  8. Grácia, X., Martin, R., 10.1088/0305-4470/38/5/009, J. Phys. A: Math. Gen. 38 2005 1071–1087 (2005) Zbl1062.70030MR2120932DOI10.1088/0305-4470/38/5/009
  9. Koon, W., Marsden, J., Poisson reduction for nonholonomic mechanical systems with symmetry, Reports on mathematical physics 42 1998 101–134 (1998) Zbl1120.37314MR1656278
  10. Krupková, O., Musilová, J., 10.1088/0305-4470/34/18/313, J. Phys. A: Math. Gen. 34 2001 3859–3875 (2001) MR1840850DOI10.1088/0305-4470/34/18/313
  11. Marle, C.-M., Various approaches to conservative and nonconservative nonholonomic systems, Reports on mathematical physics 42 1998 211–229 (1998) Zbl0931.37023MR1656282
  12. Rosenberg, R., Analytical dynamics of discrete systems, Plenum press 1997 (1997) MR0512893
  13. Śniatycki, J., 10.5802/aif.2006, Annales de L’Institut Fourier 53 2003 2257–2296 (2003) Zbl1048.53060MR2044173DOI10.5802/aif.2006
  14. van der Schaft, A., Maschke, B., 10.1016/0034-4877(94)90038-8, Reports on mathematical physics 34 (2) 1994 225–233 (1994) Zbl0817.70010MR1323130DOI10.1016/0034-4877(94)90038-8

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