Browsing by Author "Maddocks, J.H."
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Item Hamiltonian Dynamics of a Rigid Body in a Central Gravitational Field(1990) Wang, L.S.; Krishnaprasad, Perinkulam S.; Maddocks, J.H.; ISRThis paper concerns the dynamics of a rigid body moving under the influence of a central gravitational field. Explicit account is taken of effects arising because of the finite extent of the body. The hamiltonian framework of the problem is exploited to elucidate questions concerning approximation, symmetry, Poisson reduction, relative equilibria, and associated stability problems.Item On the Kinematics and Control of Wheeled Mobile Robots.(1987) Alexander, James C.; Maddocks, J.H.; ISRA wheeled mobile robot is here modelled as a planar rigid body that rides on an arbitrary number of wheels. The connections between the rigid body motion of the robot, and the steering and driving controls of wheels are developed. In particular, conditions are obtained that guarantee that rolling without skidding or sliding can occur. Explicit differential equations are derived to describe the rigid body motions that arise from rolling trajectories. The simplest wheel configuration that permits control of arbitrary rigid body motions is determined. The question of slippage due to misalignment of the wheels is investigated based on a physical model of friction. Examples are presented to illustrate the models.Item On the Maneuvering of Vehicles.(1987) Alexander, James C.; Maddocks, J.H.; ISREquations are derived to govern the motion of vehicles which move on rolling wheels. A relation between the centers of curvature of the trajectories of the wheels and the center of rotation of the vehicle is established. From this relation the general kinematic laws of motion are derived. Applications to questions of offtracking (the difference between the trajectories of the front and back wheels of the vehicle) and optimal steering (how to steer around a tight corner) are considered.Item Restricted Quadratic Forms, Inertia Theorems and the Schur Complement.(1987) Maddocks, J.H.; ISRThe starting point of this investigation is the properties of restricted quadratic forms, x^TAx, x {IS A MEMBER OF} S {IS A SUBSET OF} {m DIMERNSIONAL SPACE}, where A is an m x m real symmetric matrix, and S is a subspace. The index theory of Heatenes (1951) and Maddocks (1985) that treats the more general Hilbert space version of this problem is first specialized to the finite-dimensional context, and appropriate extensions, valid only in finite-dimensions, are made. The theory is then applied to obtain various inertia theorems for matricea and positivity tests for quadratic forms. Expressions for the inertial of divers symmetrically partitioned matrices are described. In particular, an inertia theorem for the generalized Schur complement is given. The investigation recovers, links and extends several, formerly disparate, results in the general area of inertia theorems.Item Steady Rigid-Body Motions in a Central Gravitational Field(1991) Wang, L.S.; Maddocks, J.H.; Krishnaprasad, Perinkulam S.; ISRIn recent work, the exact dynamic equations for the motion of a finite rigid body in a central gravitational field were shown to be of Hamiltonian form with a noncanonical structure. In this paper, the notion of relative equilibrium is introduced based upon this exact model. In relative equilibrium, the orbit of the center of mass of the rigid body is a circle, but the center of attraction may or may not lie at the center of the orbit. This feature is used to classify great-circle and non-great-circle orbits. The existence of non-great-circle relative equilibria for the exact model is proved from various variational principles. While the orbital offset of the non-great-circle solutions is necessarily small, a numerical study reveals that there can be significant changes in orientation away from the classic Lagrange relative equilibria, which are solutions of an approximate model.