关于变分学中逆问题的研究
On the Inverse Problem in Calculus of Variations
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摘要: 本文研究了变分学中的逆问题.通过变积概念的引入,给出了系统地研究变分学中逆问题的一种新途径.将这种方法应用于线弹性动力学和粘性流体力学中,建立了各自的变分原理和广义变分原理.Abstract: The inverse problem in calculus of variation is studied.By introducing a newconcept called Varialional Integral,a new method to systematically study the inverse problem in calculus of rariations is given.Using this new method to the elastodynamics and hydrodynamics of viscous fhuids some kinds of variaiional principles and generalized variational prineiples are obtained respectively.
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Key words:
- variational princple /
- variational integral /
- inverse problem
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[1] 刘殿魁、张其浩,弹性理论中非保守间题的一般变分原理,力学学报,6(1981). [2] 钱伟长,《变分法及有限元》(上册),科学出版社(1980). [3] 胡海昌,《弹性力学的变分原理及其应用》.科学出版社(1981). [4] Gurtin.M.E.,Variational PrinciPlos for linear clasto-dynamics,Arch.Rat.Mech.,16(1964). [5] 罗恩,关于线弹性动力学中各种Gortin型变分原理,中国科学(A),9(1987). [6] Lin,C.C.(林家翘)and L.Rubinow,on the flow behind curved shocks,Journal of Mathematics and Physics,27(1948),105-129. [7] 钱伟长,粘性流体力学的变分原理和广义变分原理,应用数学和力学,5(3)(1984),305-322. -
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