Bifurcations and limit cycles due to self‐excitation in nonlinear systems with joint friction: Initialization of isolated solution branches via homotopy methods.

Autor:	Kappauf, Jonas, Hetzler, Hartmut
Předmět:	NONLINEAR systems ALGEBRAIC equations DYNAMICAL systems LIMIT cycles FRICTION
Zdroj:	PAMM: Proceedings in Applied Mathematics & Mechanics; Nov2019, Vol. 19 Issue 1, pN.PAG-N.PAG, 1p
Abstrakt:	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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
Externí odkaz:	Zobrazit plný text záznamu Plný text