Trajectories of a rigid body are considered where the centre of the body is fixed or moves over any space form (that is, a sphere of any radius, the equivalent with negative curvature, and fiat 3D space). Open loop controls maintain the required trajectory. Three applications illustrate the concepts developed in the thesis. Firstly, a symmetric body moves over a sphere to any position and attitude where one torque maintains a constant rotation. The integration is achieved by specializing the double cover formulation of a rotation over any space form and by using a Lax pair consisting of the Hamiltonian and momentum vectors expressed in the same frame of reference. Secondly, an asymmetric satellite follows a planned trajectory to its target attitude. The natural rotation of an asymmetric satellite cannot be expressed analytically so two simple rotation modes are used; an eigenaxis and a spin stabilized rotation (with optimized spin rate). The profile of the angular velocity is adjusted by reparameterizing time to accelerate and stop the satellite. The controls required for this are compared with those required to maintain the planned rotation. In the final application, a search pattern of linear runs and turns is planned for an Autonomous Underwater Vehicle (AUV) which moves at an oblique angle. Thrusts and torques exerted by the AUV provide the controls to overcome drift, dissipative forces, conservative forces and to accelerate the surrounding fiuid out of the way. The latter consideration changes the effective inertia in different directions and the centre of mass of the AUV. Drift arises from the conservation of momentum and its evaluation is dependent on maintaining a constant inertia matrix along the trajectory. Dissipative forces are expressed in a generalized format applicable to other situations, such as aircraft and vehicles which do not have a preferred direction. In addition, the velocity profile is adjusted to smoothly join the linear run to the turn without coming to rest. The controls required to achieve this search pattern are determined.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:632860 |
| Date | January 2014 |
| Creators | Linton, Carol |
| Publisher | University of Reading |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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