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Higher-Order Systems in Classical Mechanics
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184 b
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Higher-order Systems in Classical Mechanics provides a valuable account of the problems in Newtonian mechanics characterized by higher-order Lagrangians which play a role in diverse areas of physics ranging from generalized electrodynamics to string models of elementary particles. In addition to the usual treatment of the direct problem of variational calculus, the solution of the inverse problem is also discussed with special attention to the existence of Lagrangian and Hamiltanian representations of ordinary and partial differential equations. Starting from the traditional treatment of classical mechanics, the authors make a smooth transition to topics like Hamiltonian formulation and Hamilton-Jacobi theory of degenerate higher-order systems. Addressing, in particular, the interest of physicists, equal emphasis is given on both point- and continuum mechanics. As an interesting curiosity, it is demonstrated that Lagrangians with fractional derivatives can bring non-conservative forces within the framework of action principle. A comprehensive introduction is presented for studying the variational/Noether symmetries of dynamical systems.
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