Acta Mechanica Sinica

, Volume 9, Issue 4, pp 345–353 | Cite as

A new method for the construction of a Lagrangian

  • Gao Puyun
  • Guo Zhongheng


In this paper, the necessary condition for the existence of a Lagrangian for the ordered direct analytic representation of a system of second-order ordinary differential equations on a connected domain is given. Under that condition, a new method for the construction of the Lagrangian is proposed. The domain of definition of the constructed Lagrangian might be diminished.

Key Words

Lagrangian mechanics inverse problems 


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  1. [1]
    Jacobi CG. Zur Theorie der Variationensrechnung und der Differentialgleichungen, 1837Google Scholar
  2. [2]
    Helmholtz H:J Reine Angew Math. 1887, 100, 137Google Scholar
  3. [3]
    Santilli RM. Foundations of Theoretical Mechanics I. New York: Springer, 1978MATHGoogle Scholar
  4. [4]
    Mei Fengxiang. Studies on Nonholonomic Dynamics. Beijing: Beijing Institute of Technology Press, 1987Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1993

Authors and Affiliations

  • Gao Puyun
    • 1
  • Guo Zhongheng
    • 1
  1. 1.Department of MathematicsPeking UniversityBeijingChina

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