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Invariant Manifolds and Resonances in a Synchronous Motor

We consider a five-dimensional, time-periodic system of ordinary differential equations describing an electro-mechanical model of a miniature synchronous motor. This system consist of a one-degree of freedom Hamiltonian system and an exponentially stable linear system, the two being coupled by periodic perturbations.
For such systems we prove the existence of a periodic solution and discuss its stability behaviour. Using Center Manifold Theory the problem can be reduced to a two-dimensional, time-periodic system which is studied with the help of averaging techniques.
We prove Ljapunov stability of the periodic solution and establish a large subset of the domain of attraction by studying capture and passage through resonance phenomena. The actual computations in the case of the model considered involve extensive use of computer algebra systems. By consequence, a regular rotation of the synchronous motor is shown for a large set of initial conditions.
For details see D. Tognola: Invariant Manifolds, Passage through Resonance, Stability and a Computer Assisted Applictaion to a Synchronous Motor, PhD Thesis ETH No. 12744, 1998.

Contacts:

D. Tognola, Prof. U. Kirchgraber

Electronic Contacts:

tognola@math.ethz.ch

Last Update:

04/07/97

Responsible:

Professor or Project Leader:           : Prof. Dr. Urs Kirchgraber
Institute or Independent Professorship : Independent Professorship of Mathematics
Department                             : Department of Mathematics

Comments to the ETH Research Report administration : Sat Jun 19 16:30:35 1999

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author Michele Marcionelli and design: Michele Marcionelli