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Modelling and Simulation of Conservative Dynamical Systems by Computer Algebra Assisted Lagrangian Mechanics
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Conservative dynamical systems is modelled with Lagrangian mechanics using Maple TM with the KTH developed plug-in symbolic package Sophia and simulated using Matlab®. Two double pendulum configurations and an object in a Keplerian orbit is studied. Motions and phase portraits are analysed, and numerical verifications of Kepler’s laws are performed. Properties concerning chaos is determined partly by examining sensitivity to initial conditions and it is shown that the 2D pendulum exhibits non-periodic behaviour whilst the 3D pendulum exhibits chaotic behaviour. Kepler’s laws are reproduced under certain assumptions. Finally, the applicability of Lagrangian mechanics when applied to conservative dynamical systems is evaluated.

Place, publisher, year, edition, pages
2017. , 80 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-210793OAI: oai:DiVA.org:kth-210793DiVA: diva2:1120027
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Available from: 2017-07-05 Created: 2017-07-05 Last updated: 2017-07-07Bibliographically approved

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CiteExportLink to record
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  • apa
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