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Applied Mathematics and Mechanics

, Volume 15, Issue 8, pp 755–765 | Cite as

Integral invariants of a holonomic dynamical ststem

  • Naseer Ahmed
Article
  • 17 Downloads

Abstract

This paper uses Poincaré's formalism to study the integral invariants of a conservative holonomic dynamical system. Introducing new parameters for the asynchronous variation, a generalization of the Poincaré and Poincaré-Cartan integral invariants is presented.

Key words

analysis mechanics holonomic dynamical system integral invariants synchronous asynchronous 

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References

  1. [1]
    Ahmed, N. Some problems in the dynamics of nonholonomic systems, Ph. D. Thesis, Quaid-i-Azam University, Islamabad, Pakistan (1986).Google Scholar
  2. [2]
    Arnold, V. I.,Mathematical Methods of Classical Mechanics, Springer-Verlag, New York Inc. (1978).Google Scholar
  3. [3]
    Benavent, R., Poincaré-Cartan integral invariant for constrained system,Ann. Phys.,118, 2 (1979), 476–489.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Cetaev, N. G., On the equations of Poincaré,Prikl. Mat. Meh.,5 (1941), 253–262.Google Scholar
  5. [5]
    Djukić, Dj. S., Integral invariants in classical nonconservative mechanics,Acta Mechanica,23, 3 (1975), 291–296.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Dobronravove, V. V., Integral-invariants of the analytical mechanics in nonholonomic coordinates,Dokl. Akad. Nauk. SSSR,XLVI (1945), 196–199.Google Scholar
  7. [7]
    Duan, L. and L. Young, About basic integral variants of holonomic nonconservative dynamical systems.Acta Mechanica Sinica,7, 2 (1991), 178–185.Google Scholar
  8. [8]
    Gantmacher, F. R.,Lectures in Analytical Mechanics, Mir Publishers, Moscow (1970).Google Scholar
  9. [9]
    Ghori, Q. K. and M. Hussain, Generalization of Hamilton-Jacobi theorem.Z. Angew. Math. Phys.,25, (1974), 536–540.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Ghori, Q. K. and N. Ahmed, Hamilton's principle for nonholonomic systems,Z. Angew. Math. Mech.,74, 2 (1994), 137–140.zbMATHMathSciNetGoogle Scholar
  11. [11]
    Pars, L. A.,A Treatise on Analytical Dynamics, Heinemann London (1968).Google Scholar
  12. [12]
    Poineré, H., Sur nue forme nouvelle des équations de la mécanique,C. R. Acad. Sci., Paris,132 (1901), 369–371.Google Scholar
  13. [13]
    Vujanovic, B., Conservation laws of dynamical systems via d'Alember's principle.Int. J. Non-Linear Mech.,13 (1978), 185–197.zbMATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    Whittaker, E. T.,A Treatise on Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press (1927).Google Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Naseer Ahmed
    • 1
  1. 1.Mathematics DepartmentQuaid-i-Azam UniversityIslamabadPakistan

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