Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 15 of 15 for “"geometric mechanics"”.
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Stochastic Geometric Mechanics and Symmetry
We explore the interaction between geometry, symmetry, and randomness in stochastically perturbed mechanical systems, in Hamiltonian as well as Lagrangian (variational) formulations. On the Hamiltonian side, we discuss a stochastic Kepler problem with a noisy angular momentum vector. We show that …
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Geometric Mechanics of Active Particles
Abstract Geometrical methods play an important role in classical dynamics, most notably in the dynamical preservation of symplecticity in Hamiltonian systems. In this way, dynamics derived from a Hamiltonian function admit energy-conserving integration schemes with an error that remains bounded in …
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A groupoid approach to geometric mechanics
… we further develop the theory of Lagrangian mechanics on algebroids. Our approach is based on the use of vector bundle connections, which leads to new expressions for the canonical equations and structures on Lie algebroids and their duals. The case of a compressible fluid is of particular …
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Geometric Mechanics, Ideal Hydrodynamics, and the Locomotion of Planar Shape -Changing Aquatic Vehicles
… the dynamics of this model in the context of geometric mechanics, demonstrating in particular that the system comprising a free deformable body and an assembly of point vortices possesses a Hamiltonian structure, and study the energetics of forward locomotion and turning through numerical …
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Foundations of the Geometric Mechanics Udwadia-Kalaba Framework for Rigid Body Constrained Motion Analysis
… of rigid bodies on nonlinear manifolds in the geometric mechanics framework. This approach simultaneously treats rotational and translational motion in a unified method without encountering singularites or non-uniqueness, issues that would arise were attitude parameterization sets used. The …
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Constrained Motion Analysis and Control of Spacecraft Asteroid Hovering with Formulation Extension in Geometric Mechanics Framework
… Then, the formulation is extended in the geometric mechanics framework to account for rigid body spacecraft asteroid hovering. Constraints are developed and applied for fully constrained and under-constrained asteroid hovering. The fully constrained solutions provided by the UK fundamental …
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Global Formulation and Control of a Class of Nonholonomic Systems
… motion of a class of non-holonomic systems using geometric mechanics, that provide us an efficient way to formulate and analyze the dynamics and their temporal evolution on the configuration manifold. The kinematics equations of the system, viewed as a rigid body, are constrained by the …
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Optimal control problems on lie groups with symmetry breaking cost functions
… of symmetry group reduction in the field of geometric mechanics. Our main contribution is a reduced sufficient condition for optimality that relies on the nonexistence of conjugate points. Coordinate formulae are derived for computing conjugate points in the reduced Hamiltonian system, and we …
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Attitude control via structural vibration : an application of compliant robotics
… tools drawn from differential geometry and geometric mechanics, which can be intimidating but which provide a comprehensive and powerful framework for understanding a wide range of locomotion problems fundamental to robotics and control theory. These tools allow us to make succinct …
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Solar Sailing Adaptive Control Around the Earth-Moon Lagrange Point L4 for Stellar Observations
… reflectivity control devices are proposed in the geometric mechanics formalism of the Special Euclidean group SE(3) and its tangent bundle TSE(3).</p>
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Topological chaos and chaotic mixing of viscous flows
… are explained from the point of view of geometric mechanics using transport through lobes. These lobes are made of segments of invariant manifolds of the periodic points that are generators of the ghost rods. A variety of the concentration-based measures, the important parameters of their …
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Rare events and dynamics in non-equilibrium systems
… this thesis we develop a general theory of the geometric mechanics of a broad class of microstructured continuum systems. Specifically, we consider systems with configuration spaces that are either Lie groups, or homogeneous spaces. We demonstrate that this theory, which we call a generalised …
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An Invariant Extended Kalman Filter for Indirect Wind Estimation Using a Small, Fixed-Wing Uncrewed Aerial Vehicle
Atmospheric sensing tasks, including measuring the thermodynamic state (pressure, temperature, and humidity) and kinematic state (wind velocity) of the atmospheric boundary layer (ABL) can aid in numerical weather prediction, help scientists assess climatological and topological features over a …
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Coupled Dynamics in the Cislunar Region and Spacecraft Attitude Prediction in a Higher-Fidelity Model
<p>The cislunar region of space is a complex, multi-body dynamical environment that cannot be modeled trivially. Traditional point-mass assumptions made to simplify the mission design process may be insufficient for accurately predicting spacecraft motion in environments where orbit-attitude …
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Robust Spacecraft Autonomy for Deep Space Exploration in Special Euclidean Group SE(3)
… work has explored these benefits within the geometric mechanics framework, demonstrating that robust filtering is possible using an unscented Kalman filter (UKF) on SE(3) and its tangent bundle \TSE. Furthermore, a novel filtering method in the field of rigid body dynamics, the discriminative …