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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Acta mechanica 49 (1983), S. 81-94 
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The wobblestone is a generalized form of a top with distinct inertias and a nonspherical surface at the point of contact to the horizontal plane on which it moves. Some wobble-stones exhibit a curious property of allowing steady rotation about the vertical principal inertia axis only when rotated in one direction, while other wobblestones exhibit repeated reversals of the direction of rotation after being spun. Here, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model. The equations are formulated in a manner suitable for numerical integration. The major observed properties of the motion of these asymmetrical tops are demonstrated in numerical simulations. The results lead to a better understanding of their complex and fundamentally nonlinear motion.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2013-08-31
    Description: From the control point of view, spacecraft are classified into two main groups: those for which the spacecraft is fully defined before the control system is designed; and those for which the control system must be specified before certain interchangeable parts of a multi-purpose spacecraft are selected for future missions. Consideration is given to both classes of problems.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: NASA-CR-161368
    Format: application/pdf
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  • 3
    Publication Date: 2014-10-01
    Description: A dynamic analysis is presented for a spin stabilized spacecraft employing four radial wire antennas with tip masses, a configuration first employed in the IMP-J spacecraft. The use of wires in place of the usual booms represents the ultimate in weight reduction at the expanse of flexibility. The satellite is modelled as a 14 degree of freedom system, and the linearized equations of motion are found. The lowest order vibrational modes and natural frequencies of the gyroscopically coupled system are then determined. Because the satellite spin rate is decreased by antenna deployment, a spin-up maneuver is needed. The response of the time varying mode equations during spin-up is found, for the planar modes, in terms of Bessel functions and a Struve function of order -1/4. Because tables of the latter are not readily available, the particular solution is expressed in various forms including an infinite series of Bessel functions and a particularly useful asymptotic expansion.
    Keywords: SPACE VEHICLES
    Type: X-732-73-233 , NASA-TM-X-70584
    Format: application/pdf
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  • 4
    ISSN: 1573-2878
    Keywords: Observation cost ; quadratic cost ; LQG problems ; optimal observation times
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Feedback control is sometimes applied to a dynamic system operating in a stochastic environment under circumstances where only a limited number of observations can be made. The optimal positioning of ana priori fixed number of observations is considered. A direct approach to this problem yields a dynamic programming functional equation, while a second approach involving an ancillary observation cost leads to a rapid and practical numerical solution.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1573-2878
    Keywords: System identification ; observer identification ; pole placement ; state space realization ; Markov parameters ; observer Markov parameters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero corresponding to a deadbeat observer. In this formulation, the Markov parameters of the observer are first identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to realize a state space model of the system. The basic mathematical formulation is derived, and numerical examples are presented to illustrate the proposed method.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1573-2878
    Keywords: Optimal control ; robotics ; path planning ; maximum principle ; multi-point boundary value problems ; multiple shooting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of the time-optimal control of robot manipulators is of importance because of its potential for increasing the productivity of assembly lines. This work is part of a series of papers by the authors on this topic using direct and indirect methods of optimization. A cylindrical robot or a spherical polar robot constrained to the horizontal plane is considered, and optimal solutions for radial maneuvers are generated. Indirect methods are employed in order to establish the switching structure of the solutions. The results show that even such apparently simple maneuvers as extension or retraction of a robot with a prismatic joint can produce very complex optimal solutions. Time-optimal retraction can exhibit ten different switching structures with eight switching points and two singular arcs.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1573-2878
    Keywords: Optimal control theory ; perturbation methods ; Lie series ; Poisson series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Concepts of programmability and compact programmability are defined relative to a class of modified Poisson series. Lie-series-based canonical perturbation methods from astrodynamics are applied to the Hamiltonian system boundary-value problem, and more usual methods are applied to the perturbed Hamilton-Jacobi-Bellman partial differential equation, in order to obtain a complete set of equations for the perturbed optimal feedback control law for both infinite-time and finite-time regulator problems. The relative advantages of each approach are evaluated. A major aim of the paper is to determine the largest class of perturbations, within the set of Poisson series, for which the equations can be derived on a computer by symbolic manipulation. The more general the class, the more accurate the perturbation solution can be, for a given order. The solutions developed are complete; all that remains is to program them in order to have computerized derivations of the optimal nonlinear feedback control laws.
    Type of Medium: Electronic Resource
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  • 8
    Publication Date: 2018-06-05
    Description: The dynamic response to operational maneuvers of spinning symmetric spacecraft with radial and axial booms was analyzed as part of the prelaunch dynamic analysis of the ISEE-3 spacecraft placed in a halo orbit around an Earth-Sun libration point, and later renamed ICE when it was directed to fly-by comet Giacobini-Zinner. The results presented use simple spacecraft models, and frequently give predictions that are good and easily obtained when the results from using a general purpose multibody dynamics program were very time consuming to obtain. Deployment of radial booms, spin-up after partial deployment, stationkeeping, and trajectory changes are analyzed. The latter two can involve both axial thrusting and pulsed radial thrusting once per revolution.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: ESA Proceedings of the Second International Symposium on Spacecraft Flight Dynamics; p 13-18
    Format: application/pdf
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  • 9
    Publication Date: 2011-08-16
    Description: A dynamic analysis is presented for a spin-stabilized spacecraft employing four radial wire antennas with tip masses. The satellite is modelled as a 14-degree-of-freedom system, and the linearized equations of motion are found. The lowest-order vibrational modes and natural frequencies of the gyroscopically coupled system are then determined. Because the satellite spin rate is decreased by antenna deployment, a spin-up maneuver is needed. The response of the time-varying mode equations during spin-up is found for the planar modes in terms of Bessel functions and a Struve function of order -0.25. The particular solution is expressed in various forms, including an infinite series of Bessel functions and a particularly useful asymptotic expansion. An error formula for the latter is derived, showing that it gives good accuracy. A simple approximation to the complementary function is obtained using the Wenzel-Kramers-Brillouin method, and the phase error in the approximation is shown to be small.
    Keywords: ASTRODYNAMICS
    Format: text
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  • 10
    Publication Date: 2011-08-19
    Description: With a sufficiently great number of sensors and actuators, any finite dimensional dynamic system is identifiable on the basis of input-output data. It is presently indicated that, for conservative nongyroscopic linear mechanical systems, the number of sensors and actuators required for identifiability is very large, where 'identifiability' is understood as a unique determination of the mass and stiffness matrices. The required number of sensors and actuators drops by a factor of two, given a relaxation of the identifiability criterion so that identification can fail only if the system parameters being identified lie in a set of measure zero. When the mass matrix is known a priori, this additional information does not significantly affect the requirements for guaranteed identifiability, though the number of parameters to be determined is reduced by a factor of two.
    Keywords: SPACECRAFT DESIGN, TESTING AND PERFORMANCE
    Type: Journal of the Astronautical Sciences (ISSN 0021-9142); 33; 95-118
    Format: text
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