General dynamics of a large class of flexible satellite systems

Lips, K. W.; Modi, V. J.

doi:10.1016/0094-5765(80)90011-9

Cited by 17 publications

(6 citation statements)

References 2 publications

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“…1). The reason why the I model predicts such a "good" energy drift is because it contains the elastic configuration dependence in the mass matrix given in (15). Indeed, without these terms, the value of e^ R^S increases to 23.8 with no discernible difference in the simulation results.…”

Section: T I F> 15smentioning

confidence: 97%

“…They are defined analogously to equations (13) and (14) with: 8c " = 2 P"a?"" a=l a=l 8H""= 2 v" "p^"p (15) We observe that the argument of the second summation in (15^) is a quadratic function of elastic variables q^^. Its inclusion is necessary to preserve the positive-definiteness of the augmented inertia matrix.…”

Section: (7)mentioning

confidence: 99%

“…Interestingly, the geometric stiffening effect was included long ago in the treatment of planar rotating beams by Likins et al [12], Vigneron [13] and Kaza and Kvatemik [14]. Since then, a number of problems deahng with multibody systems in a variety of applications have been addressed (see for example, Lips and Modi [15], Hughes and Fung [16], Simo and Vu-Quoc [17], Banerjee and Lemak [18], and Walrapp [19]. All of these works incorporate geometric stiffening in the governing equations, although via different routes.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

Damaren¹,

Sharf

1995

Journal of Dynamic Systems, Measurement, and Control

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Several important issues relevant to modeling of flexible-link robotic manipulators are addressed in this paper. First, we examine the question of which inertial nonlinearities should be included in the equations of motion for purposes of simulation. A complete model incorporating all inertial terms that couple rigidbody and elastic motions is presented along with a rational scheme for classifying them. Second, the issue of geometric nonlinearities is discussed. These are terms whose origin is the geometrically nonlinear theory of elasticity, as well as the terms arising from the interbody coupling due to the elastic deformation at the link tip. Accordingly, a general way of incorporating the well-known geometric stiffening effect is presented along with several schemes for treating the elastic kinematics at the joint interconnections. In addition, the question of basis function selection for spatial discretization of the elastic displacements is also addressed. The finite element method and an eigenfunction expansion techniques are presented and compared. All issues are examined numerically in the context of a simple beam example and the Space Shuttle Remote Manipulator System. Unlike a single-link system, the results for the latter show that all terms are required for accurate simulation of faster maneuvers. Hence, the conclusions of the paper are contrary to some of the previous findings on the validity of various models for dynamics simulation of flexible-body systems. 74/Vol. 117, MARCH 1995 Transactions of the ASME Copyright © 1995 by ASME Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 09/16/2013 Terms of Use: http://asme.org/terms Journal of Dynamic Systems, Measurement, and Control MARCH 1995, Vol. 117/75 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 09/16/2013 Terms of Use: http://asme.org/terms 76/Vol. 117, MARCH 1995 Transactions of the ASME Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 09/16/2013 Terms of Use: http://asme.org/terms Journal of Dynamic Systems, Measurement, and Control MARCH 1995, Vol. 117/83 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 09/16/2013 Terms of Use: http://asme.org/terms

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Section: T I F> 15smentioning

confidence: 97%

Section: (7)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

Damaren¹,

Sharf

1995

Journal of Dynamic Systems, Measurement, and Control

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“…The writings of Bainum and Kumar (1982), Diarra and Bainum (1987), Dubowsky and Sunada (1982), Hale and Meirovitch (1982), Ho and Herber (1985), Hughes (1979), Huston (1980Huston ( , 1981, Ibrahim and Modi (1986), Kane, Ryan, and Banerjee (1987), Levinson (1982), Likins (1975), Lips and Modi (1980), Rajaram and Junkins (1985), Rosen, Loewy and Mathcw (1987), Shabana (1985), Wu, Haug, and Kim (1989), and of Yoo and Haug (1986) represent a sampling of this research.…”

Section: Flexible Multibody Systemsmentioning

confidence: 97%

Multibody Dynamics — Modeling and Analysis Methods

Huston

1991

Applied Mechanics Reviews

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A review of recent developments in multibody dynamics modeling and analysis is presented. Multibody dynamics is one of the fastest growing fields of applied mechanics. Multibody systems are increasingly being employed as models of physical systems such as robots, mechanisms, chains, cables, space structures, and biodynamic systems. Research activity in multibody dynamics has stimulated research in a number of subfields including formulation methods, system modeling, numerical procedures, and graphical representations. These are also discussed and reviewed.

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“…Problems of the aerospace industry and robotics stimulate the development of new methods for mathematical modeling and control design for complex mechanical systems with elastic elements. In particular, it is a well-known fact that the vibrations of flexible parts of satellites influence significantly their dynamics, so that a rigid body model is not acceptable in stability and control investigations for such distributed parameter systems (see, e.g., [2,11,14]). This brings the motivation for studying the controllability and stabilization issues for infinite-dimensional mathematical models of flexible structures with strings, beams, and plates.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Stabilization of a Rotating Mechanical System with Elastic Plates

Zuyev

Novikova

2018

IFAC-PapersOnLine

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A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled nonlinear ordinary and partial differential equations. The operator form of this system is represented as an abstract differential equation in a Hilbert space. A feedback control law is constructed such that the corresponding infinitesimal generator is dissipative.

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General dynamics of a large class of flexible satellite systems

Cited by 17 publications

References 2 publications

Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

Multibody Dynamics — Modeling and Analysis Methods

Modeling and Stabilization of a Rotating Mechanical System with Elastic Plates

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