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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Direct inversion of rigid-body rotational dynamics

The global linearization (inversion) of rigid-body rotational dynamics is reviewed and representations in terms of quaternions and direction cosines are compared. Certain properties common to quaternions and direction cosines that make their use preferable to Euler angles and that simplify the inversion procedure are described. Applications of the inversion procedure for state estimation and attitude control are discussed. To avoid complexities caused by aerodynamics, an example of direct inversion for linear feedback control of spacecraft attitude is given.

Bach, Ralph↗
NASA NTRS1990

Direct inversion of rigid-body rotational dynamics

The global linearization (inversion) of rigid-body rotational dynamics is reviewed, and representations in terms of quaternions and direction cosines are compared. Certain properties common to quaternions and direction cosines that make their use preferable to Euler angles and that simplify the inversion procedure are described. Applications of the inversion procedure for state estimation and attitude control are discussed. To avoid complexities caused by aerodynamics, an example of direct inversion for linear feedback control of spacecraft attitude is given.

Bach, Ralph↗
NASA NTRS1975

Point-connected rigid bodies in a topological tree

The purpose of the present paper is to explore the applicability of several methods of analytical mechanics to the modern problem of formulating generic equations of motion of a point-connected set of rigid bodies in a topological tree, in order to compare the results of the previously published Hooker-Margulies/Hooker equations. The unexpected result of the inquiry is the discovery that with the substitution of a key kinematical identity from the Hooker and Margulies vector-dyadic equations for the multiple-rigid-body tree, identical equations emerge from each of four quite different derivation procedures.

Likins, P. W.↗
NASA NTRS1988

Finite volume computation of unsteady inviscid rotational transonic flows past airfoils in rigid body motion

Unsteady inviscid transonic flow over airfoils in arbitrary rigid body motion is analyzed numerically by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables are used to form the numerical dissipation terms to stabilize the scheme. Unsteady calculations are started from converged steady-state solutions as initial conditions. Nonreflective boundary conditions are imposed on the far-field boundaries. Results are presented and, where possible, validated against available numerical and experimental data for airfoils subjected to a step change in angle of attack, airfoils oscillating and plunging in transonic flow, and airfoils immersed in a time-varying free stream.

Damodaran, Murali↗
NASA NTRS1974

The acoustic far-field of rigid bodies in arbitrary motion

The far-field sound produced by a rigid body in arbitrary motion, with shock discontinuities close to the body, is studied. The analysis is based on the work of Ffowcs Williams and Hawkings (1969). An expression for the far-field sound pressure is obtained in the form of surface and line integrals carried out over a contracting sphere and its intersection with the body and shock surfaces. It is also found that in addition to the quadrupole distribution, the discontinuities in Lighthill stress at the shock, the fluid stresses at the body surface, and the curvatures (principal and mean) of the body and shock surfaces contribute to the sound field. Two examples are worked out.

Farassat, F.↗
NASA NTRS1983

Normal mode study of the earth's rigid body motions

In this paper it is shown that the earth's rigid body (rb) motions can be represented by an analytical set of eigensolutions to the equation of motion for elastic-gravitational free oscillations. Thus each degree of freedom in the rb motion is associated with a rb normal mode. Cases of both nonrotating and rotating earth models are studied, and it is shown that the rb modes do incorporate neatly into the earth's system of normal modes of free oscillation. The excitation formula for the rb modes are also obtained, based on normal mode theory. Physical implications of the results are summarized and the fundamental differences between rb modes and seismic modes are emphasized. In particular, it is ascertained that the Chandler wobble, being one of the rb modes belonging to the rotating earth, can be studied using the established theory of normal modes.

Chao, B. F.↗
NASA NTRS2013

Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies

Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is ·discussed, and illustrative simulation results are presented.

Stoneking, Eric T.↗
NASA NTRS1974

Hamilton/Jacobi perturbation methods applied to the rotational motion of a rigid body in a gravitational field

The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.

Fitzpatrick, P. M.↗
NASA NTRS1979

Gravitational waves from rotating and precessing rigid bodies - Simple models and applications to pulsars

An axially symmetric, torque-free rigid body, rotating and precessing, emits gravitational quadrupole radiation at two frequencies, omega and 2 omega, corresponding to the l = 2, m = 1,2 spherical harmonics. The paper presents explicitly the waveforms of the two polarizations at both frequencies. From observations of gravitational waves, one can derive information about the body's orientation and its precession amplitude. Electromagnetic radiation emitted by a spot fixed on the surface of the body arrives in pulses at a mean frequency Omega which is typically different from omega. If the body is not axially symmetric but the amplitude of the precession is small, the gravitational radiation at the lower frequency omega is split into two frequencies on either side of the electromagnetic pulse frequency. Explicit waveforms for the two polarizations in this case are also presented.

Zimmermann, M.↗
NASA NTRS2004

Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

Shivarama, Ravishankar↗
DOE OSTI2026

Energy-conserving contact dynamics of nonspherical rigid-body particles

Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.

Discrete element method↗