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Bifurcations and limit cycles due to self‐excitation in nonlinear systems with joint friction: Initialization of isolated solution branches via homotopy methods
Author(s) -
Kappauf Jonas,
Hetzler Hartmut
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900412
Subject(s) - homotopy analysis method , homotopy , limit (mathematics) , initialization , limit cycle , nonlinear system , mathematics , limit point , algebraic number , point (geometry) , numerical continuation , mathematical analysis , physics , computer science , pure mathematics , bifurcation , geometry , quantum mechanics , programming language
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.