A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Robust Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.

Procedural aspects of modeling the dynamics of a three wheeled vehicle using ADAMS-CAR

We describe in some detail the process of development of a dynamic model of a three wheeled vehicle using ADAMS-CAR. We first describe the rigid body model, and then the modeling of structural flexibilities. The aim of this report is to document procedural details of such modeling, with a view to presenting more research and development oriented investigations in the future. The contents of this report may also be of interest to practicing engineers engaged in multi-body dynamics modeling of wheeled vehicles.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Structural stability of slender aerospace vehicles: Part I Mathematical modeling

A detailed mechanics based model is developed to analyze the problem of structural instability in slender aerospace vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic pressure and the propulsive thrust of the vehicle. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. Condition under which a flexible body with internal stress waves behaves like a perfect rigid body is derived. Two methods are developed for finite element discretization of the system: (1) A time-frequency Fourier spectral finite element method and (2) h-p finite element method. Numerical results using the above methods are presented in Part II of this paper. (C) 2010 Elsevier Ltd. All rights reserved.

Accurate prediction of interfacial residues in two-domain proteins using evolutionary information: Implications for three-dimensional modeling

With the preponderance of multidomain proteins in eukaryotic genomes, it is essential to recognize the constituent domains and their functions. Often function involves communications across the domain interfaces, and the knowledge of the interacting sites is essential to our understanding of the structure-function relationship. Using evolutionary information extracted from homologous domains in at least two diverse domain architectures (single and multidomain), we predict the interface residues corresponding to domains from the two-domain proteins. We also use information from the three-dimensional structures of individual domains of two-domain proteins to train naive Bayes classifier model to predict the interfacial residues. Our predictions are highly accurate (approximate to 85%) and specific (approximate to 95%) to the domain-domain interfaces. This method is specific to multidomain proteins which contain domains in at least more than one protein architectural context. Using predicted residues to constrain domain-domain interaction, rigid-body docking was able to provide us with accurate full-length protein structures with correct orientation of domains. We believe that these results can be of considerable interest toward rational protein and interaction design, apart from providing us with valuable information on the nature of interactions. Proteins 2014; 82:1219-1234. (c) 2013 Wiley Periodicals, Inc.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

Attitude estimation using moment invariants

The problem of estimating the three-dimensional rotational parameters of a rigid body from its monocular image data has been considered using the method of moment invariants. Second- and third-order moment invariants are used to construct the feature vector for the scale and orientation independent identification of the camera view axis direction in the body-fixed reference frame. The camera rotation angle about the view axis is derived from second-order central moments. The relative attitude of the rigid body is then expressed in terms of quaternion parameters to model the outputs of a video sensor in attitude control simulations. Experimental results and simulation outputs are presented using the mathematical model of a spacecraft.

Mean field lattice model for adsorption isotherms in zeolite NaA

Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate-adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a "coverage-dependent interaction'' model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate-adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions. (C) 1999 American Institute of Physics. [S0021-9606(99)70515-5].

A game theoretical multiple resource interaction approach to resource allocation in an air campaign

In this paper we propose a multiple resource interaction model in a game-theoretical framework to solve resource allocation problems in theater level military campaigns. An air raid campaign using SEAD aircraft and bombers against an enemy target defended by air defense units is considered as the basic platform. Conditions for the existence of saddle point in pure strategies is proved and explicit feedback strategies are obtained for a simplified model with linear attrition function limited by resource availability. An illustrative example demonstrates the key features.

The central region of meso-3,4-diphenylhexane-2,5-dione

As with 1,2-diphenylethane (dpe), X-ray crystallographic methods measure the central bond in meso-3,4-diphenylhexane-2,5-done (dphd) as significantly shorter than normal for an sp(3)-sp(3) bond. The same methods measure the benzylic (ethane C-Ph) bonds in dphd as unusually long for sp(3)-sp(2) liaisons. Torsional motions of the phenyl rings about the C-Ph bonds have been proposed as the artifacts behind the result of a 'short' central bond in dpe. While a similar explanation can, presumably, hold for the even 'shorter' central bond in dphd, it cannot account for the 'long' C-Ph bonds. The phenyl groups, departing much from regular hexagonal shape, adopt highly skewed conformations with respect to the plane constituted by the four central atoms. It is thought that-the thermal motions of the phenyl rings, conditioned by the potential wells in which they are ensconced in the unit cell, are largely libratory around their normal axes. In what appears to be a straightforward explanation under the 'rigid-body' concept, it appears that these libratory motions of the phenyl rings, that account, at the same time, for the 'short' central bond, are the artifacts behind the 'long' measurement of the C-Ph bonds. These motions could be superimposed on torsional motions analogous to those proposed in the case of dpe. An inspection of the ORTEP diagram from the 298 K data on dphd clearly suggests these possibilities. Supportive evidence for these qualitative explanations from an analysis of the differences between the mean square displacements of C(1) and C(7)/C(1a) and C(7a) based on the 'rigid-body model' is discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Dynamical configurations and bistability of helical nanostructures under external torque

We study the motion of a ferromagnetic helical nanostructure under the action of a rotating magnetic field. A variety of dynamical configurations were observed that depended strongly on the direction of magnetization and the geometrical parameters, which were also confirmed by a theoretical model, based on the dynamics of a rigid body under Stokes flow. Although motion at low Reynolds numbers is typically deterministic, under certain experimental conditions the nanostructures showed a surprising bistable behavior, such that the dynamics switched randomly between two configurations, possibly induced by thermal fluctuations. The experimental observations and the theoretical results presented in this paper are general enough to be applicable to any system of ellipsoidal symmetry under external force or torque.

Study of dendrite growth in a rotational flow field

A numerical model to study the growth of dendrites in a pure metal solidification process with an imposed rotational flow field is presented. The micro-scale features of the solidification are modeled by the well-known enthalpy technique. The effect of flow changing the position of the dendrite is captured by the Volume of Fluid (VOF) method. An imposed rigid-body rotational flow is found to gradually transform the dendrite into a globular microstructure. A parametric study is carried out for various angular velocities and the time for merger of dendrite arms is compared with the order estimate obtained from scaling.

mulPBA: an efficient multiple protein structure alignment method based on a structural alphabet

The increasing number of available protein structures requires efficient tools for multiple structure comparison. Indeed, multiple structural alignments are essential for the analysis of function, evolution and architecture of protein structures. For this purpose, we proposed a new web server called multiple Protein Block Alignment (mulPBA). This server implements a method based on a structural alphabet to describe the backbone conformation of a protein chain in terms of dihedral angles. This sequence-like' representation enables the use of powerful sequence alignment methods for primary structure comparison, followed by an iterative refinement of the structural superposition. This approach yields alignments superior to most of the rigid-body alignment methods and highly comparable with the flexible structure comparison approaches. We implement this method in a web server designed to do multiple structure superimpositions from a set of structures given by the user. Outputs are given as both sequence alignment and superposed 3D structures visualized directly by static images generated by PyMol or through a Jmol applet allowing dynamic interaction. Multiple global quality measures are given. Relatedness between structures is indicated by a distance dendogram. Superimposed structures in PDB format can be also downloaded, and the results are quickly obtained. mulPBA server can be accessed at www.dsimb.inserm.fr/dsimb_tools/mulpba/.