Deriving generalized variational principles in general mechanics by using Lagrangian multiplier method
- 42 Downloads
By using the involutory transformations, the classical variational principle—Hamiltonian principle— of two kinds of variables in general mechanics is advanced and by using undetermined Lagrangian multiplier method, the generalized variational principles and generalized variational principles with subsidiary conditions are established. The stationary conditions of various kinds of variational principles are derived and the relational problems discussed.
Keywordsnonholonomic system holonomic system two kinds of variables generalized variational principle generalized variational principle with subsidiary condition
Unable to display preview. Download preview PDF.
- 1.Qian Lingxi, Principle of complementary energy (in Chinese),Scientia Sinica, 1950,1(1):449.Google Scholar
- 2.Hu Haichang, On some variational principles in the theory of elasticity and the theory of plasticity,Scientia Sinica, 1955, 4 (1):33.Google Scholar
- 3.Chien Wei-zang, Research on the generalized variational principles in elasticity theory and its application in the calculation of finite element,Mechanics and Practice, 1979,(1): 16,(2): 18.Google Scholar
- 5.Liang Lifu., On a problem of analytical dynamics of nonholonomic systems, inProceedings of International Conference on Applied Mechanics (ed. Zheng, Z.M.), Beijing: Pergamon Press, 1989, 65–69.Google Scholar
- 6.Rumyantsev V. V., Ttranslated by Mei Fengxiang, Euler and variational principles in mechanics (in Chinese),Developments in Mechanics, 1993, 23(1): 86.Google Scholar
- 9.Chien Wei-zang,Variational Methods and Finite Element Methods (in Chinese), Beijing: Science Press, 1980, 1–150.Google Scholar
- 10.Liang Lifu, Zhang Zimao, On some flexibility of undetermined Lagrange multiplier method (in Chinese),Acta Mechanica Sinica, 1989, 21(1): 111.Google Scholar