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Type of Document	Dissertation
Author	Fetecau, Razvan Constantin
Author's Email Address	van AT acm.caltech.edu
URN	etd-05222003-110241
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-05222003-110241
Title	Variational methods for nonsmooth mechanics
Degree	PhD
Option	Applied Mathematics
Advisory Committee	Advisor Name Title Jerrold E. Marsden Committee Chair Donald S. Cohen Committee Member Niles Pierce Committee Member Thomas Y. Hou Committee Member
Keywords	discrete mechanics rigid-body collisions multisymplectic geometry symplectic integrators
Date of Defense	2003-05-14
Availability	unrestricted
Abstract In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Next, we develop the foundations of a multisymplectic treatment of nonsmooth classical and continuum mechanics. This work may be regarded as a PDE generalization of the previous formulation of a variational approach to collision problems. The multisymplectic formulation includes a wide collection of nonsmooth dynamical models such as rigid-body collisions, material interfaces, elastic collisions, fluid-solid interactions and lays the groundwork for a treatment of shocks. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically and the longtime stable energy behavior typical of variational methods is demonstrated.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    01thesis.pdf 513.30 Kb 00:02:22 00:01:13 00:01:04 00:00:32 00:00:02   02vita.pdf 74.91 Kb 00:00:20 00:00:10 00:00:09 00:00:04 < 00:00:01