Bifurcations and limit cycles due to self‐excitation in nonlinear systems with joint friction: Initialization of isolated solution branches via homotopy methods. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Kappauf, Jonas; Hetzler, Hartmut
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900412
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The main objective of this contribution is finding isolated stationary solutions, e.g. equilibria or limit cycles, in dynamical systems. Usually, NEWTON‐type methods are applied for solving the resulting algebraic equation system. Here, the most difficult point is finding adequate initial conditions that are providing a solution on the isolated branch. So, there is a need for a more straight forward manner of initialising the continuation of isolated solutions. Within this contribution, homotopy methods are applied. The crucial point is to define a simplified version of the problem F ( x ; λ), which can be continuously transformed into the original one. As an example, limit cycles of a friction oscillator including COULOMB damping is discussed and two types of homotopy maps are addressed to obtain a starting point for their continuation.