Integral Manifolds of the Charged Three-Body Problem

Zaman, M., 2017, [Groningen]: Rijksuniversiteit Groningen. 131 p.

Research output: ThesisThesis fully internal (DIV)Academic

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  • Title and contents

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  • Chapter 1

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  • Chapter 2

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  • Chapter 3

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  • Chapter 4

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  • Chapter 5

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  • Chapter 6

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  • Chapter 7

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  • Summary

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  • Samenvatting

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  • Acknowledgments

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  • Bibliography

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  • Biography

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  • Complete thesis

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  • Propositions

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  • Mohammad Zaman
This thesis is dedicated to the study of the In-
tegral Manifolds of the Charged Three-Body Problem. My aim is to
give a mathematical analysis of the physical mechanical system that
consists of three charged particles moving in space and interacting via
a Coulomb potential. The system is mathematically described by a
Hamiltonian on a 18-dimensional phase space. A physical mechanical
system may have symmetries and consequently conserved quantities
or integrals. Fixing the values of the integrals defines the integral
manifolds. Depending on the values, the integral manifolds may have
different topologies. Changes can occur at critical values of the in-
tegrals. My main aim is to find these critical values for the charged
three-body problem. Projecting the integral manifolds from the phase
space to the configuration space, we get so called Hill regions. The
Hill regions hence consists of the admissible positions for given values
of the integrals. Thus we get in particular information about the pos-
sibility of collisions for given values of the integrals. Part of the aim
of this thesis is study whether and how the Hill regions of the charged
three-body problem change topology at critical values. The topology
of the integral manifolds has been studied in detail for the gravitati-
onal three-body problem by McCord, Meyer and Wang. This thesis
comprises the first steps in a similar study for the charged three-body
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Waalkens, Holger, Supervisor
  • Hoveijn, Igor, Co-supervisor
  • Jaffé, C. (Charles), Assessment committee, External person
  • Eckhardt, Bruno, Assessment committee, External person
  • Broer, Hendrik, Assessment committee
Award date31-Mar-2017
Place of Publication[Groningen]
Print ISBNs978-90-367-9706-1
Electronic ISBNs978-90-367-9705-4
Publication statusPublished - 2017

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