Abstract.
This paper deals with the generalization of the field method to non-holonomic systems whose motion is subject to either non-linear constraints or those of a higher order, while their motion is modeled by the generalized Lagrange equations of the second kind. Two examples are given to illustrate the theory.
Similar content being viewed by others
References
Pars, L.A.: A Treatise on Analytical Mechanics. London: Heinemann, 1968
Vujanovic, B.D, Jones S.E.: Variational Methods in Nonconservative Phenomena. Boston: Academic Press, 1989
Arzhanikh, I.S.: Field of Momentum. Tashkent: Nauka, 1965
Djukic Dj.S., Vujanovic B.D.: Noehter’s theory in classical nonconservative mechanics. Acta Mech, 23, 17–27 (1975)
Whittaker, E.T.: Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge: Cambridge University Press, 1904
Vujanovic B.: On a gradient method in nonconservative mechanics. Acta Mech, 34, 167–179 (1979)
Vujanovic, B.: On the integration of nonconservative Hamilton’s dynamical equations. Int J Engng Sci, 19, 1739–1747 (1981)
Rumyantsev, V.V., Sumbatov, A.S.: On the problem of a generalization of the Hamilton-Jacobi method for nonholonomic systems. ZAMM, 58, 477–481 (1978)
Dooren, R.: Generalized methods for nonholonomic systems with applications in various fields of classical mechanics. In: Theoretical and Applied Mechanics Proceedings of the 14th IUTAM Congress, Delft, 1976-8-30-9-4. Amsterdam-New York-Oxford: North Holland Pub Co, 1976 373–391
Mei, F.X.: A field method for solving the equation of motion of nonholonomic systems. Acta Mechanica Sinica, 5, 260–269 (1989)
Mei, F.X.: On the integration methods of non-holonomic dynamics. Int J of Non-Linear Mech, 35, 229–238 (2000)
Mei, F.X.: On one method of the integration of equations of motion of non-holonomic systems with constraints of a higher order. Appl Math Mech, 55, 691–695 (1991) (in Russian)
Djukic, D.j.: On a generalized form of the Lagrange equations of the second kind. Appl Math Mech, 37, 156–159 (1973) (in Russian)
Kovacic, I.: Application of the field method to the non-linear theory of vibrations. J Sound Vib, 264, 1073–1090 (2003)
Kovacic, I.: A field method in the study of weakly non-linear two degree-of-freedom oscillatory systems. J Sound Vib, 27, 464–468 (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
The project supported by the Ministry of Science, Technologies and Development, Republic of Serbia (1874)
Rights and permissions
About this article
Cite this article
Kovacic, I. On the field method in non-holonomic mechanics. ACTA MECH SINICA 21, 192–196 (2005). https://doi.org/10.1007/s10409-005-0018-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-005-0018-x