Abstract
In this chapter, two-dimensional shooting diagrams are introduced for visualization of manifolds of periodic solutions and their bifurcations. A general class of nonlinear oscillators under smooth, nonsmooth, and impulsive loadings is considered. The corresponding boundary value problems are formulated by introducing the triangular wave temporal argument. The Duffing oscillator with no linear stiffness (Ueda circuit) is considered for illustration. It is shown that the temporal mode shape of the loading is responsible for qualitative features of the dynamics, such as transitions from regular and random motions. The important role of unstable periodic orbits is discussed.
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© 2010 Springer-Verlag Berlin Heidelberg
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Pilipchuk, V.N. (2010). NSTT and Shooting Method for Periodic Motions. In: Nonlinear Dynamics. Lecture Notes in Applied and Computational Mechanics, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12799-1_12
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DOI: https://doi.org/10.1007/978-3-642-12799-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12798-4
Online ISBN: 978-3-642-12799-1
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