Student Projects
Geometric Mechanics, Project Archives

2009

• Alemi, A. [2009]. Laplace-Runge-Lenz Vector
• Censi, A. [2009]. Symplectic Camels And Uncertainty Analysis
• Crane, K. [2009]. Project Proposal
• Crane, K. [2009]. Toward Spacetime Adaptive Variational Integrators
• Jacobs, H. [2009]. Momentum and Energy Transfer between Coupled Mass-Spring Chains
• Moore, A. [2009]. Two Approaches Utilizing Invariant Manifolds To Design Trajectories For DMOC Optimization
• Perkins, R. [2009]. Geometric Approach to the Motion of a Charged Particle in a Toroidal Magnetic Field
• Rufat, D. [2009]. Squirming Sphere in an Ideal Fluid
• Safavi-Naeini, A. [2009]. Dielectric Interactions with Electromagnetic Radiation
• Tyranowski, T. M. [2009]. Hamilton-Pontryagin variational integrators
• Werne, T. [2009]. Constrained Lagrangian Circuits

2007

• Lepine, C. [2007]. Time-Dependent Invariant Manifolds Theory and Computation
• Pekarek, D. [2007]. Forced Variational Collision Integrators
• Tao, M. [2007]. A Systematic Illustration on Reduction of N-body Problem with Application to Molecular Systems
• Whitehead, K. [2007]. Multisymplectic Geometry on the Three Dimensional General Schrodinger Equation

2005

• Carson, J. [2005]. Examining Geometric Integration for Propagating Orbit Trajectories with Nonconservative Forcing
• Du Toit, P. [2005]. The Astrojax Pendulum and the N-Body Problem on the Sphere: A study in reduction, variational integration, and pattern evocation
• Gayme, D. [2005]. Stabilization of Free Rigid Body Dynamics Using a Single Internal Rotor
• Hudson, N. [2005]. Mobility of a Simple Hinged Body in an Ideal Fluid
• Lamperski, A. [2005]. Comparing Distributed Primal-Dual Algorithms for Discrete Variational Mechanics and Internet Congestion Control
• Miller, A. [2005]. Holonomic Quantum Computing and Geometric Quantum Phase
• Roumi, F. [2005]. Solid Mechanics Applications of Geometric Mechanics
• Stern, A. [2005]. Discrete Electromagnetism with DEC
• Wolf, M. [2005]. Incorporating Nonholonomic Constraints in Basic Geometric Mechanics Concepts
• Yu, X. [2005]. Hamiltonian Structure of the 2D Surface Quasi-Geostrophic Equation
• Zhang, L. [2005]. On Whitham's Averaging Method

2003

• Brunton, S. [2003]. Algorithmic Implementation of Energy Methods for Classifying Stability of Relative Equilibria
• Chen, L. [2003]. Holonomic Quantum Computation
• Hopkins, A. [2003]. How does a falling cat turn over?
• Kelly, A. [2003]. A look at Suris Approach to Integrable Discretizations
• Liang, Y. [2003]. A Review of Geometry in Robotic Locomotion
• Pritchard, J. [2003]. Geometry of the Kaluza-Klein theory of Electromagnetism
• Randall, P. [2003]. Controlled Lagrangians and the Inverted Pendulum on a Cart
• Shadden, S. [2003]. Steering Laws for UAVs
• Spanos, D. [2003]. An Attempt at a Unified Variational Principle for Dynamics and Optimal Control of an Underactuated Mechanical System
• Van Handel, R. [2003]. Dissipation from noisy Hamiltonians
• Waydo, S. [2003]. Swimming in Magnetic Fields: A Case Study
• Yavari, A. and J. E. Marsden [2003]. Geometry of Configurational Forces

2001

• Bhat, H. [2001]. Algebraic Quantization
• Del Vecchio, D. [2001]. *Missing Title*
• Fung, J. [2001]. To Study the Kelvin-Noether theorem and its applications to fluid mechanics
• Prajna, S. [2001]. Developments in the Theory of Implicit Hamiltonian Systems
• Ross, S. D. [2001]. Mechanical Integrators from a Discrete Variational Principle

1999

• Grebeck, M. [1999]. Jacobi Identity for the Poisson Bracket
• Murphey, T. [1999]. Geometric Phase in Holonomic and Nonholonomic Systems - Two examples
• Thweatt, A. [1999]. Phase Portrait Analysis for Physical Systems
• Vela, P. [1999]. *Missing Title*
• Wang, Y. [1999]. Formal Instability of 3D Inviscid flows

1998

• Fax, A. [1998]. Approximation of Constrained Dynamics via Augmented Potentials
• Porter, M. A. [1998]. The KdV Equation

1996

• Adiwidjaja, H. [1996]. The Reduced Energy-Momentum Method
• Bullo, F. [1996]. On Controllability and Symmetries in Simple Mechanical Systems
• Wang, Y. [1996]. Application of Energy-Momentum Method to Rotating Strings
• Yeung, S. [1996]. Simmulation of a Chaotic Planar Double Pendulum

1995

• Adiwidjaja, H. [1995]. On the Korteweg de-Vries equation
• Anshelevich, M. [1995]. The Duality in the Formulation of a Classical Particle in a Yang-Mills Field
• Baesu, E. [1995]. The Falling Cat
• Brown, A. [1995]. Casey's Geometrical Derivation of Lagrange's Equations
• Bullo, F. [1995]. Invariant Affine Connections and Controllability on Lie Groups
• Chamberlain [1995]. Additional Topics in Differential Geometry with an Aim Toward Further Studies of the General Theory of Relativity
• Dutton, Z. [1995]. Bifurcations of Periodic Orbits
• Faradjian, T. [1995]. Generating Functions of Lagrangian Submanifolds
• Jakobsen, E. R. [1995]. Hamiltonian Systems in Fluid Mechanics
• Jones, R. [1995]. Symplectic Integrators and the Dynamics of the Rigid Body
• Love, E. [1995]. Unconditionally Stable Algorithms for Rigid Body Dynamics that Exactly Preserve Energy and Momentum
• LU, J. [1995]. Conserving Integrators by Generating Function
• Mizel, A. [1995]. Nonuniqueness of the Lagrangian Function
• Nadeau, J. C. [1995]. *Missing Title*
• Nath, D. [1995]. *Missing Title*
• Pribik, P. N. [1995]. On the Role of Tori in Mechanics
• Wang, Y. [1995]. A Particle in a Rotating Hoop
• Yeung, S. [1995]. The Triple Spherical Pendulum

1994

• Coleman, C. P. [1994]. The Search for Stable Equilibria on Coadjoint Orbits and Applications to Dissipative Processes
• Creagh, S. [1994]. Calogero Systems and Reductions
• De Luca, J. [1994]. Construction of a Poisson Bracket for Maxwell's Equations using Reduction
• Hershman, A. [1994]. Path Integral for a Particle in a Box
• Landsberg, A. [1994]. Normal Forms and Resonances
• Nassiri-Toussi, K. [1994]. Stability of Hamiltonian Systems: Energy-Momentum method and Effect of Dissipation
• Pierce, M. K. [1994]. Symplectic Integrators
• Wendlandt, J. [1994]. Nonholonomic Mechanical Systems

1993

• Burgess, H. [1993]. Sophus Lie and Symmetry
• Coleman, C. P. [1993]. Chaos in A Spacecraft Passive Attitude Maneuver and the Marsden Energy Sink
• Ernst, D. [1993]. Chaos in Mappings
• Godbole, D. [1993]. Stabilization of Rigid Body Dynamics
• Hershman, A. [1993]. Linear Hamiltonian Systems and the Hopf Map
• Lygeros, J. [1993]. Dynamics of Nonholonomic Systems: a Sphere Rolling on a Spinning Table
• Nassiri-Toussi, K. [1993]. Equations of Motion in the Field of a Magnetic Monopole: An Example of Phase-Space Reduction on Cotangent Bundles
• Reinsch, M. [1993]. Geometric Phases in the Motion of Particles on Hoops
• Shlyakhtenko, D. [1993]. Generating Functions of Canonical Transformations

1992

• Alexander, P. [1992]. *Missing Title*
• Filippini, R. [1992]. Coadjoint Orbits and Representation Theory
• Jalnapurkar, S. [1992]. The Lagrange D'Alembert Equations and Constraints
• Kheradvar, R. [1992]. *Missing Title*
• Koon, W. S. [1992]. *Missing Title*
• Perlmutter, M. [1992]. Noncommutative Integration of Hamiltonian Systems

1990

• Branson, B. [1990]. Smale's Horseshoe
• Flynn, W. [1990]. A Simple Calculator of the Born-Pauli-Infeld Bracket for Maxwell's Equations including boundaries
• Goroff, D. [1990]. Twist Maps, Billiards, and Celestial Mechanics
• Malitz, S. [1990]. Cyclic evolution in Quantal Systems and the adiabatic Approximation: the Physics vs the Math Point of View
• Montgomery, R. [1990]. Existence of Minima in the Calculus of Variations
• Pierce, M. K. [1990]. Poisson Brackets on Superfluids
• Rio, R. [1990]. Reduction and Hamiltonian Structures on Duals of Lie Algebras with Specialization to the Heavy Top
• Rychlik, M. [1990]. Klimontovich Functions and Poisson Manifolds
• Tarnow, N. [1990]. Chaos in Buckling Beams and Duffing's Equations
• Travish, G. [1990]. Does Berry's Phase Affect Particles in Accelerators?
• Walsh, W. [1990]. Path Planning for a Satellite with Two Momentum Wheels
• Wonchoba, W. E. [1990]. A Geometric Analysis of Foucault's

1989

• Applegate, K. [1989]. The Kirchhoff, Clebsch and Steklov tops (Following Camassa and Holm)
• Bartels, C. [1989]. Charged Particles and Paradox in the Equivalence Principle
• Doeff, E. [1989]. Rotating Systems in Goldstein and Landau and Lifshitz
• Hirschberg, P. [1989]. Another Twist to Berry's Bead on a Hoop
• Morehead, J. [1989]. Rotation of an Asymmetric Free Rigid Body About its Middle Axis
• O'Keefe, M. [1989]. The Kaluza-Klein Theory of Projected Fields
• Pradeep, A. K. [1989]. Generating Functions: Goldstein vs Marsden

1988

• Bond, B. [1988]. The Foucault Pendulum Analyzed with an Eye Towards Berry's Phase
• Kerswell, R. [1988]. Stability of the Inverted Pendulum: A Topological Explanation by Mark Levi
• Lin, F. [1988]. The Free Rigid Body: Reduction, Quantization condition, and Prequantization
• Lin, F. [1988]. Symplectic Reduction and Geometric Prequantization of Cotangent Bundles
• Longcope, D. W. [1988]. The Vlasov-Poisson Equation and the Energy Casimir Method