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Variational iterational method in stability analysis of beams under nonconservative forces

Glabisz W., Jarczewska K., Zielichowski-Haber W.

Archives of Civil and Mechanical Engineering

2013

Vol. 13, no. 1

82--87

The aim of this paper is to demonstrate the effectiveness of VIM in the analysis of the stability of prismatic and nonprismatic (multisegmental) Euler–Bernoulli beams under static nonconservative loads. The application of VIM to the analysis of beam problems may lead to solutions which can form the basis for the evaluation of the quality of the numerical methods used in the problems. The general Lagrange multipliers for the Euler–Bernoulli beam equation are presented. The convergence of VIM for the multipliers is discussed and an exemplary solution to the problem of the stability of the multisegmental beam under nonconservative loads is presented.

Symbolic computation of variational symmetries in optimal control

Gouveia P. D., Torres D. F., Rocha E. A.

Control and Cybernetics

2006

Vol. 35, no 4

831-849

We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of nonconservative external forces. As an application, we obtain eight independent first integrals for a sub-Riemannian nilpotent problem (2,3,5,8).