×

Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics. (English) Zbl 1149.70311

Summary: We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D’Alembert’s principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.

MSC:

70E55 Dynamics of multibody systems
PDFBibTeX XMLCite
Full Text: DOI HAL

References:

[1] Appell, P. 1899 Sur une Forme Generale des Equations de la Dynamique. <i>C. R. Acad. Sci. Paris</i>&nbsp;<b>129</b>, 459–460.
[2] Dirac, P.A.M. 1964 Lectures in quantum mechanics. New York: Yeshiva University. · Zbl 0141.44603
[3] Gauss, C.F. 1829 Uber ein neues allgemeines Grundgsetz der Mechanik. <i>J. Reine Ang. Math.</i>&nbsp;<b>4</b>, 232–235.
[4] Gibbs, J.W. 1879 On the fundamental formulae of dynamics. <i>Am. J. Math.</i>&nbsp;<b>2</b>, 49–64. · JFM 11.0643.01
[5] Lagrange, J.L. 1787 Mechanique analytique. Paris: Mme Ve Courcier.
[6] Pars, L.A. 1979 A treatise on analytical dynamics. pp. 14, Woodridge, CT: Oxbow Press · Zbl 0125.12004
[7] Udwadia, F.E. & Kalaba, R.E. 1992 A new perspective on constrained motion. <i>Proc. R. Soc. A</i>&nbsp;<b>439</b>, 407–410. · Zbl 0766.70011
[8] Udwadia, F.E. & Kalaba, R.E. 1996 Analytical dynamics: a new approach. Cambridge, UK: Cambridge University Press. · Zbl 0875.70100
[9] Udwadia, F.E. & Kalaba, R.E. 2001 Explicit equations of motion for mechanical systems with nonideal constraints. <i>ASME J. Appl. Mech.</i>&nbsp;<b>68</b>, 462–467. · Zbl 1110.74717
[10] Udwadia, F.E. & Kalaba, R.E. 2002 On the foundations of analytical dynamics. <i>Int. J. Nonlin. Mech.</i>&nbsp;<b>37</b>, 1079–1090, (doi:10.1016/S0020-7462(01)00033-6). · Zbl 1346.70011
[11] Udwadia, F.E., Kalaba, R.E. & Hee-Chang, E. 1997 Equation of motion for constrained mechanical systems and the extended D’Alembert’s principle. <i>Q. Appl. Math.</i>&nbsp;<b>LV</b>, 321–331. · Zbl 0881.70012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.