Titlebook: An Introduction to Modern Variational Techniques in Mechanics and Engineering; B. D. Vujanovic,T. M. Atanackovic Textbook 2004 Springer Sc

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https://doi.org/10.1007/978-3-322-83450-8ilton canonical differential equations . UPi oq, where .(. , ...,.,.l, ...,.) is th e Hamiltonian function. In writing (2.1.1) we assumed that the nonconservative (nonpotential) generalized forces are equal to zero :

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Die Vernetzung sozialer Einheitenof conservat ive and purely nonconservative dynamical systems. The basic idea of this approach is to consider the transformation properties of the Lagrange-D’Alembert principle with respect to the infinite simaltransform at ion of the generalized coordinates and time. It is of interest to note that

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https://doi.org/10.1007/978-3-476-03451-9method for solving the canonical differential equat ions of mot ion. In addition, a variety of approximate methods can be built up , based upo n this method , for solving nonlinear problems for which an exact, complete solu tion of the Hamilton-J acobi nonlinear partial differential equa t ion is no

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https://doi.org/10.1007/978-3-476-03451-9e is based upon the . characteristics of motion; that is, the relations between its scalar and vector characteristics are considered simultaneously in one particular inst ant of time. The problem of describing the global characteristics of motion has been reduced to the integration of differential e

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https://doi.org/10.1007/978-3-476-03451-9 We shall cons ider in particular the cases in which the initi al or terminal configur at ions (or both) ar e not sp ecified . Also, it may happen that t he time interval in which the evolut iona ry process is t aking place is not given . For these cases the Hamiltonian principle usually produces ch

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https://doi.org/10.1007/978-3-663-16065-6r of degrees of freedom of a dynamical system. In this chapter we will consider several import ant situations in which the generalized coordinates are . but are restricted by given auxiliary conditions. Namely, it is not uncommon in th e analysis of applied variational problems to be faced with the

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https://doi.org/10.1007/978-0-8176-8162-3Optimal control; Transformation; calculus; dynamical systems; ksa; mechanics; optimization; stability

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https://doi.org/10.1007/978-3-663-16065-6In this section we shall use the results presented so far to formulate several variational principles for t he equations describing deformations and the optimal shape of elastic columns. We shall use the classical (Bernoulli-Euler) rod theory as well as generalized rod theories. The variational principles that we will formulate will be used to

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Variational Principles for Elastic Rods and ColumnsIn this section we shall use the results presented so far to formulate several variational principles for t he equations describing deformations and the optimal shape of elastic columns. We shall use the classical (Bernoulli-Euler) rod theory as well as generalized rod theories. The variational principles that we will formulate will be used to