Previous |  Up |  Next

Article

Keywords:
nonholonomic constraints; d’Alembert’s principle
Summary:
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.
References:
[1] Bates, L.: Examples of singular nonholonomic reduction. Reports on Mathematical Physics 42 1998 231–247 DOI 10.1016/S0034-4877(98)80012-8 | MR 1656283 | Zbl 0931.37022
[2] Bates, L., Śniatycki, J.: Nonholonomic reduction. Reports on Mathematical Physics 32 1993 99–115 DOI 10.1016/0034-4877(93)90073-N | MR 1247165
[3] Cantrijn, F., de León, M., Marrero, J., de Diego, D.: Reduction of constrained systems with symmetries. Journal of mathematical physics 40 1999 795–820 DOI 10.1063/1.532686 | MR 1674283
[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 MR 1617882
[5] de León, M., de Diego, D.: Mechanical systems with nonlinear constraints. International journal of theoretical physics 36 (4) 1997 979–995 DOI 10.1007/BF02435796 | MR 1445410
[6] Giaquinta, M., Hildebrandt, S.: Calculus of Variations I. Number 310 in Grundlehren der mathematischen Wissenschaften. Springer-Verlag 1996 MR 1368401
[7] Goldstein, H., Poole, C., Safko, J.: Classical mechanics. Addison-Wesley, third edition 2002 MR 0043608
[8] Grácia, X., Martin, R.: Regularity and symmetries of nonholonomic systems. J. Phys. A: Math. Gen. 38 2005 1071–1087 DOI 10.1088/0305-4470/38/5/009 | MR 2120932 | Zbl 1062.70030
[9] Koon, W., Marsden, J.: Poisson reduction for nonholonomic mechanical systems with symmetry. Reports on mathematical physics 42 1998 101–134 MR 1656278 | Zbl 1120.37314
[10] Krupková, O., Musilová, J.: The relativistic particle as a mechanical system with non-holonomic constraints. J. Phys. A: Math. Gen. 34 2001 3859–3875 DOI 10.1088/0305-4470/34/18/313 | MR 1840850
[11] Marle, C.-M.: Various approaches to conservative and nonconservative nonholonomic systems. Reports on mathematical physics 42 1998 211–229 MR 1656282 | Zbl 0931.37023
[12] Rosenberg, R.: Analytical dynamics of discrete systems. Plenum press 1997 MR 0512893
[13] Śniatycki, J.: Orbits of families of vector fields on subcartesian spaces. Annales de L’Institut Fourier 53 2003 2257–2296 DOI 10.5802/aif.2006 | MR 2044173 | Zbl 1048.53060
[14] van der Schaft, A., Maschke, B.: On the hamiltonian formulation of nonholonomic mechanical systems. Reports on mathematical physics 34 (2) 1994 225–233 DOI 10.1016/0034-4877(94)90038-8 | MR 1323130 | Zbl 0817.70010
Partner of
EuDML logo