Dynamics of a System of Bodies with Program-Variable Configuration

Zakrzhevskii, A. E.; Matarazzo, James M.; Khoroshilov, V. S.

doi:10.1023/b:inam.0000031919.06748.ee

Cited by 12 publications

(6 citation statements)

References 5 publications

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“…It is impossible to model such perturbations within the framework of the dynamics of a system of bodies. A general mathematical model of a spacecraft with a gravity-gradient boom that is being deployed in a programmed manner has been constructed in [2]. The dynamics of a spacecraft during the deployment of an elastic gravity-gradient boom was studied in [16].…”

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Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

Zakrzhevskii

Khoroshilov

2014

Int Appl Mech

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An unstabilized spacecraft with a pantograph structure deployed in orbit to carry solar batteries is the subject of study. The objective of the study is to construct a mathematical model of this system taking into account the elastic properties of elements of the pantograph in longitudinal and transverse directions. This model is based on the Lagrangian formalism as applied to a mechanical system with rheonomic constraints. The expressions for the coefficients of the equations of motions are obtained using Mathematica 5 © . A Fortran application software package is used for numerical simulation of dynamic processes. This package can be adapted, if necessary, to study other structures. The behavior of the spacecraft during the deployment of the pantograph is numerically analyzed using different values of spacecraft parameters and the parameters of the deployment process in the gravity field.Introduction. The dynamics of reconfigurable systems is one of the promising and important research areas in mechanics [9,[11][12][13]23]. Modern spacecraft incorporate various components that are deployed in orbit (solar batteries (SB), gravity-gradient booms, antennas, etc.). Such mechanical systems are delivered to orbit compactly packaged and then are deployed there. There is literature on the deployment of elastic elements from a fixed base and from a spinning spacecraft [9,[11][12][13]23], including the deployment of a gravity-gradient boom [15,19]. In these studies, the maximum bending moments, deflections of booms, and optimal deployment time were assessed using various simplifying assumptions. Cherchas [14] studied the dynamics of spin-stabilized satellites during the extension of long flexible booms. He has determined the maximum nutation and precession angles after the deployment of the boom and its maximum bending moments and deflections, derived the equations of motion using Lagrange's equations, and discretized the elastic degrees of freedom by a modal analysis. In [20,21,24], the dynamics of deployable elastic elements is also described in terms a modal analysis with time-dependent natural modes.Banerjee and Kane [7] present a new method for simulating the motion of a beam that is being extruded from, or retracted into a rotating rigid body. In essence, the method consists of modeling the beam as a series of elastically connected rigid links and then working with equations of motion linearized in the modal coordinates for the links outside the rigid body. In [6,8], the analysis was extended to large deflections and used an order-n formulation for a variable number of bodies. The modeling has revealed that the tip deflections are very sensitive to the extrusion/retraction rate, the retraction process is less stable than the extrusion process, and the behavior of the beam is strongly dependent on the angular rate of the body.The deployment of such elements is a substantial perturbation to the motion of the spacecraft around its center of mass. It is impossible to model such perturbations within the framework of the...

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Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

Zakrzhevskii

Khoroshilov

2014

Int Appl Mech

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“…Plots illustrating the variation of characteristic variables are presented Introduction. Dynamics of reconfigurable systems is one of the promising and important areas of research in mechanics [1,2,5,[8][9][10][11]. Modern spacecraft incorporate elements that transform when in orbit (solar batteries, gravity-gradient booms, antennas, etc.).…”

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On the dynamics of deployment of an orbital structure with elastic elements

et al. 2006

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The object to be studied is a spacecraft with a deployable pantograph structure as a solar-battery carrier. The objective of research is to design a mathematical model of this structure taking the elasticity of pantograph elements into account. The Lagrangian formalism is followed. To model the dynamic processes in the system, a software package has been developed, which can be adapted, if necessary, to study deployable structures of other types. The behavior of the structure during deployment, collapse, and redeployment under the action of various perturbations is modeled numerically. Plots illustrating the variation of characteristic variables are presented Introduction. Dynamics of reconfigurable systems is one of the promising and important areas of research in mechanics [1,2,5,[8][9][10][11]. Modern spacecraft incorporate elements that transform when in orbit (solar batteries, gravity-gradient booms, antennas, etc.). Such mechanical systems are delivered into orbit compactly packaged and then are deployed into the operational configuration.Issues of current importance in research of reconfigurable systems are minimization of deployment time and energy and the effect of reconfigurable structures on the motion and attitude of the spacecraft. Also, of vital importance is mass reduction for such systems. Their elements should be considered as elastic bodies.1. Mechanical Model. The object of study is a pantograph structure consisting of two connected parallelogram-type linkages (Fig. 1). The mechanical model is a reconfigurable structure with a pantograph-like deployment mechanism mounted on a rigid body.

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“…The adapter modules are modeled by inertialess rectilinear elastic bars of certain length and cross section embedded in the bodies. Such dynamic models are of importance since they allow us to analyze the dynamics of an SV system with allowance for the elastic interaction between them during maneuvers and to estimate the dynamic loading on both the space vehicle [1] and the adapter module [2].Design models in the form of connected rigid bodies are widely used to solve applied dynamic problems for complex engineering structures [3,4,[11][12][13][14]. Such dynamic problems can mainly be solved by conducting a computational experiment [5].…”

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“…Design models in the form of connected rigid bodies are widely used to solve applied dynamic problems for complex engineering structures [3,4,[11][12][13][14]. Such dynamic problems can mainly be solved by conducting a computational experiment [5].…”

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On the nonlinear dynamics of elastically interacting asymmetric rigid bodies

Кравец

2006

Int Appl Mech

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A symmetric mathematical model is developed to describe the spatial motion of a system of space vehicles whose structure is represented by regular geometrical figures (Platonic bodies). The model is symmetrized by using the Euler-Lagrange equations of motion, the Rodrigues-Hamilton parameters, and quaternion matrix mathematics. The results obtained enable us to model a wide range of dynamic, control, stabilization, and orientation problems for complex systems and to solve various problems of dynamic design for such systems, including estimation of dynamic loading on the basic structure during maneuvers in space Introduction. Dynamic models in the form of discrete mechanical systems of asymmetric rigid bodies connected by elastic bars arise in dynamic problems for space vehicles (SVs) joined by standard adapter modules into open ( Fig. 1à) or closed chains. Closed SV chains may be either plane (triangle, square, or any other regular polygon (Fig. 1b)) or spatial (Platonic bodies: tetrahedron, octahedron, icosahedron, etc. (Fig. 1c)). The nodes of such geometrical figures are space vehicles and their edges are adapter modules. The space vehicles are modeled by asymmetric rigid bodies that experience follower forces generated by the control, stabilization, and orientation system. The adapter modules are modeled by inertialess rectilinear elastic bars of certain length and cross section embedded in the bodies. Such dynamic models are of importance since they allow us to analyze the dynamics of an SV system with allowance for the elastic interaction between them during maneuvers and to estimate the dynamic loading on both the space vehicle [1] and the adapter module [2].Design models in the form of connected rigid bodies are widely used to solve applied dynamic problems for complex engineering structures [3,4,[11][12][13][14]. Such dynamic problems can mainly be solved by conducting a computational experiment [5]. To this end, it is necessary to set up adequate mathematical models of physical processes. These models should be easily implemented on state-of-the-art computers. The key element in this model design concept is the symmetry of a model, which was understood by H. Weyl as order, perfection [6].Following the concept of symmetrization, we will develop a mathematical model to describe the spatial motion of a system of asymmetric rigid bodies connected by elastic bars into open or closed ordered chains in the form of regular polygons or polyhedrons. The model will be symmetrized by using the Euler-Lagrange equations of motion, the Rodrigues-Hamilton parameters, and quaternion matrix mathematics [7,8].1. Problem Formulation. According to the principle of removing constraints (and replacing them by their reactions), the whole variety of structures of SV systems under consideration can be reduced to a standard unified substructure consisting of an isolated spacecraft and an adapter module. This substructure is taken to be a superelement and is modeled by an inertialess elastic bar embedded in an asymmetric rigid bod...

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Dynamics of a System of Bodies with Program-Variable Configuration

Cited by 12 publications

References 5 publications

Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

Dynamics of an Unstabilized Spacecraft During the Deployment of an Elastic Pantograph Structure

On the dynamics of deployment of an orbital structure with elastic elements

On the nonlinear dynamics of elastically interacting asymmetric rigid bodies

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