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Numerical program integrating motion equation of charged particles from realistic geomagnetic field model, with trajectory calculations for solar cosmic rays
Motion equations and basic control theory applied to stability and response analyses of flexible launch vehicle using unified coordinate system and notation
Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.
Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.
Partial differential equations and matrix method for obtaining equations of motion in orbit
Numerical integration of lunar motion equations to investigate lunar theory for high precision applications and to examine motion departures from gravitational theory
Integration of equations of planetary peturbations in rectangular coordinates
Develop a model that simulates a human running in 0 G using the European Space Agency s (ESA) Subject Loading System (SLS). The model provides ground reaction forces (GRF) based on speed and pull-down forces (PDF). DESIGN The theoretical basis for the Running Model was based on a simple spring-mass model. The dynamic properties of the spring-mass model express theoretical vertical GRF (GRFv) and shear GRF in the posterior-anterior direction (GRFsh) during running gait. ADAMs VIEW software was used to build the model, which has a pelvis, thigh segment, shank segment, and a spring foot (see Figure 1).the model s movement simulates the joint kinematics of a human running at Earth gravity with the aim of generating GRF data. DEVELOPMENT & VERIFICATION ESA provided parabolic flight data of subjects running while using the SLS, for further characterization of the model s GRF. Peak GRF data were fit to a linear regression line dependent on PDF and speed. Interpolation and extrapolation of the regression equation provided a theoretical data matrix, which is used to drive the model s motion equations. Verification of the model was conducted by running the model at 4 different speeds, with each speed accounting for 3 different PDF. The model s GRF data fell within a 1-standard-deviation boundary derived from the empirical ESA data. CONCLUSION The Running Model aids in conducting various simulations (potential scenarios include a fatigued runner or a powerful runner generating high loads at a fast cadence) to determine limitations for the T2 vibration isolation system (VIS) aboard the International Space Station. This model can predict how running with the ESA SLS affects the T2 VIS and may be used for other exercise analyses in the future.
The problems associated with optimum approaches to an orbiting spacecraft at the completion of rendezvous are exacerbated when the maneuvering spacecraft is to dock with such large and extended structures as the NASA Space Station, which also has a torque equilibrium attitude due to which the docking port does not point directly into the orbital track. Attention is presently given to a candidate 'operationally optimum' approach to a local vertical-local horizontal stabilized target; this glideslope approach is derived on the basis of Hill's relative-motion equations, which have been expanded to encompass constant relative accelerations in a closed form solution. The motion is described in polar coordinates.
This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.
Equation for vortex motion including effects of buoyancy and sources with applications to tornadoes
A solution procedure is described for determining the two-dimensional, one- or two-degree-of-freedom flutter characteristics of arbitrary airfoils at large angles of attack. The same procedure is used to predict stall flutter. This procedure requires a simultaneous integration in time of the solid and fluid equations of motion. The fluid equations of motion are the unsteady compressible Navier-Stokes equations, solved in a body-fitted moving coordinate system using an approximate factorization scheme. The solid equations of motion are integrated in time using an Euler implicit scheme. Flutter is said to occur if small disturbances imposed on the airfoil attitude lead to divergent oscillatory motions at subsequent times. Results for a number of special cases are presented to demonstrate the suitability of this scheme to predict flutter at large mean angles of attack. Some stall flutter applications are also presented.
A solution procedure was developed to investigate the two-dimensional, one- or two-dimensional flutter characteristics of arbitrary airfoils. This procedure requires a simultaneous integration in time of the solid and fluid equations of motion. The fluid equations of motion are the unsteady compressible Navier-Stokes equations, solved in a body-fitted moving coordinate system using an approximate factorization scheme. The solid equations of motion are integrated in time using an Euler implicit scheme. Flutter is said to occur if small disturbances imposed on the airfoil attitude lead to divergent oscillatory motions at subsequent times. The flutter characteristics of airfoils in subsonic speed at high angles of attack and airfoils in high subsonic and transonic speeds at low angles of attack are investigated. The stall flutter characteristics are also predicted using the same procedure.
A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.
The singly-averaged differential equations of motion of a satellite are developed in terms of parameters valid for all eccentricities less than one. The perturbations included in the acceleration model are due to an aspherical central planet (zonal harmonics up to degree 20 and resonant harmonics up to degree and order 20), atmospheric drag for a time-varying atmosphere, third-body gravity (the sun and moon for an earth satellite), solar radiation pressure with shadowing, and impulsive maneuvers. Analytic averaging is used to remove short-period terms due to the aspherical central planet and third-body gravity. Numerical averaging is used to remove short-period terms due to atmospheric drag and solar radiation pressure.
Characteristic method analysis of linear system of dynamic cylindrical equation for axisymmetric motion, including rotary inertia and shear correction factor
Two body torque free gyrostat equations of rotational motion, relating rotational, spin and precession angular velocities
The coupled base motion equations of a system composed of a launch vehicle and several payloads are derived. In previous work it was shown how the special form of these equations allow for a quick and accurate solution both for the response and the loads of the system. In this paper a short-cut version of this direct integration technique is presented and evaluated. The result is a method which, depending on the nature of the structure at hand, vasilates between a full-scale coupled base motion approach and an open loop base drive method. Although completely general, the presented technique is most effective when the number of interface degrees of freedom is relatively small compared to the overall number of degrees of freedom of the system. The S.T.S.-S.T.-O.M.S. Kit system is used as an illustrative example.