Helicopter Basic Equations of Motion

2011 ◽  
pp. 21-30
Author(s):  
Ioannis A. Raptis ◽  
Kimon P. Valavanis
Keyword(s):  
Equations Of Motion ◽  
Basic Equations

scholarly journals Symmetry analysis of rotating fluid

2005 ◽  
Vol 47 (1) ◽  
pp. 65-74 ◽  
Author(s):  
K. Fakhar ◽  
Zu-Chi Chen ◽  
Xiaoda Ji
Keyword(s):  
Steady State ◽  
Infinite Number ◽  
Special Function ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Lie Theory ◽  
Rotating Fluid ◽  
Type Solution ◽  
Function Type ◽  
Basic Equations

AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

scholarly journals Construction And Test Of Thermostats And Twirlers For Molecular Rotations

2003 ◽  
Vol 58 (7-8) ◽  
pp. 377-391 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Time Reversal ◽  
Rotational Diffusion ◽  
Equations Of Motion ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Polymer Molecules ◽  
Isotropic Harmonic Oscillator ◽  
Molecular Rotations ◽  
Basic Equations ◽  
Nonlinear Elastic

The equations of motion are coupled with a dynamical variable, referred to as twirler, which randomizes the angular momentum. The equations are time-reversal invariant, just as those for the standard Gaussian, Nosé-Hoover and configurational thermostats. The derivation of the basic equations is outlined. Test calculations are performed for the two-dimensional isotropic harmonic oscillator and for a nonlinear elastic dumbbell, used as a simple model to study properties of polymer molecules. Graphs of characteristic quantities and orbits, some of which are rather intriguing, are displayed. As applications, the rotational diffusion and the influence of a shear flow on the angular velocity and the deformation of the model polymer are analyzed.

scholarly journals Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200513
Author(s):  
Andrew Jackson ◽  
Stefano Maffei
Keyword(s):  
Rotation Axis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Planetary Cores ◽  
Motional Induction ◽  
Basic Equations ◽  
Short Time ◽  
Magnetic Case

An approximation is developed that lends itself to accurate description of the physics of fluid motions and motional induction on short time scales (e.g. decades), appropriate for planetary cores and in the geophysically relevant limit of very rapid rotation. Adopting a representation of the flow to be columnar (horizontal motions are invariant along the rotation axis), our characterization of the equations leads to the approximation we call plesio-geostrophy , which arises from dedicated forms of integration along the rotation axis of the equations of motion and of motional induction. Neglecting magnetic diffusion, our self-consistent equations collapse all three-dimensional quantities into two-dimensional scalars in an exact manner. For the isothermal magnetic case, a series of fifteen partial differential equations is developed that fully characterizes the evolution of the system. In the case of no forcing and absent viscous damping, we solve for the normal modes of the system, called inertial modes. A comparison with a subset of the known three-dimensional modes that are of the least complexity along the rotation axis shows that the approximation accurately captures the eigenfunctions and associated eigenfrequencies.

scholarly journals CONSTRUCTION AND RESEARCH OF FULL BALANCE ENERGY OF VARIATIONAL PROBLEM MOTION SURFACE AND GROUNDWATER FLOWS

2017 ◽  
Vol 1 ◽  
pp. 45-52
Author(s):  
Petro Venherskyi
Keyword(s):  
Variational Problem ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Energy System ◽  
Problem Solution ◽  
Flow Energy ◽  
Balance Energy ◽  
Basic Equations ◽  
Surface And Groundwater

Based on the laws of conservation of mass and momentum the basic equations of motion with unknown quantities velocity and piezometric pressure are written. These equations are supplemented with boundary and initial conditions describing the motion of compatible flows. Based on the laws of motion continuum, received conditions contact on the common border interaction of surface and groundwater flows. Variational problems formulated compatible flow. Energy norms of basic components of variational problem are analyzed. Correctness of constructing variational problem arising from construction of the energy system of equations that allow to investigate properties of the problem solution, its uniqueness, stability, dependence on initial data and more. Energy equation of motion of surface and groundwater flows are derived and investigated. It is shown that the total energy compatible flow depends on sources that are located inside the domain or on its border.

scholarly journals A general fluid–sediment mixture model and constitutive theory validated in many flow regimes

2018 ◽  
Vol 861 ◽  
pp. 721-764 ◽  
Author(s):  
Aaron S. Baumgarten ◽  
Ken Kamrin
Keyword(s):  
Constitutive Model ◽  
Equations Of Motion ◽  
Material Point ◽  
Mixed System ◽  
Two Phase ◽  
Mixture Phase ◽  
State Behaviour ◽  
Steady Shearing ◽  
Basic Equations ◽  
Sediment Mixture

We present a thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes, developed from the basic balance laws for two-phase mixtures. The model can represent various limiting cases, such as pure fluid and dry grains. It is formulated to capture a number of key behaviours such as: (i) viscous inertial rheology of submerged wet grains under steady shearing flows, (ii) the critical state behaviour of grains, which causes granular Reynolds dilation/contraction due to shear, (iii) the change in the effective viscosity of the fluid due to the presence of suspended grains and (iv) the Darcy-like drag interaction observed in both dense and dilute mixtures, which gives rise to complex fluid–grain interactions under dilation and flow. The full constitutive model is combined with the basic equations of motion for each mixture phase and implemented in the material point method (MPM) to accurately model the coupled dynamics of the mixed system. Qualitative results show the breadth of problems which this model can address. Quantitative results demonstrate the accuracy of this model as compared with analytical limits and experimental observations of fluid and grain behaviours in inhomogeneous geometries.

scholarly journals Challenges and design choices for global weather and climate models based on machine learning

2018 ◽  
Author(s):  
Peter D. Dueben ◽  
Peter Bauer
Keyword(s):  
Deep Learning ◽  
Climate Models ◽  
Equations Of Motion ◽  
Huge Amount ◽  
Weather Forecasts ◽  
Learning Techniques ◽  
Weather And Climate ◽  
Atmospheric Data ◽  
Basic Equations ◽  
Physical Principles

Abstract. Can models that are based on deep learning and trained on atmospheric data compete with weather and climate models that are based on physical principles and the basic equations of motion? This question has been asked often recently due to the boom of deep learning techniques. The question is valid given the huge amount of data that is available, the computational efficiency of deep learning techniques and the limitations of today's weather and climate models in particular with respect to resolution and complexity. In this paper, the question will be discussed in the context of global weather forecasts. A toy-model for global weather predictions will be presented and used to identify challenges and fundamental design choices for a forecast system based on Neural Networks.

Some developments in the theory of vortex breakdown

1967 ◽  
Vol 28 (1) ◽  
pp. 65-84 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Theoretical Treatment ◽  
Stationary Waves ◽  
Flow Models ◽  
Essential Properties ◽  
Small Flow ◽  
Basic Equations

The primary aim of the analysis presented herein is to consolidate the ideas of the ‘conjugate-flow’ theory, which proposes that vortex breakdown is fundamentally a transition from a uniform state of swirling flow to one featuring stationary waves of finite amplitude. The original flow is assumed to be supercritical (i.e. incapable of bearing infinitesimal stationary waves), and the mechanism of the transition is explained on the basis of physical principles that are well established in relation to the analogous supercritical-flow phenomenon of the hydraulic jump or bore. In previous presentations of the theory the existence of appropriately descriptive solutions to the full equations of motion has only been inferred from these general principles, but here the solutions are demonstrated explicitly by means of a perturbation analysis. This has basically much in common with the classical theory of solitary and cnoidal waves, which is known to explain well the essential properties of weak bores.In § 2 the basic equations of the problem are set out and the leading results of the original theoretical treatment are recalled. The new developments are mainly presented in § 3, where an analysis of finite-amplitude waves is completed by two different methods, each serving to illustrate points of interest. The effects of small energy losses and of small flow-force reductions (i.e. wave-resistance effects) are considered, and the analysis leads to a general classification of possible phenomena accompanying such changes of integral properties in either slightly supercritical or slightly subcritical vortex flows. The application to vortex breakdown remains the focus of attention, however, and § 3 includes a careful appraisal of some experimental observations on the phenomenon. In § 4 a summary is given of a variant on the previous methods which is required when the radial boundary of the flow is taken to infinity. The main analysis is developed without restriction to particular flow models, but in § 5 the results are applied to a specific example.

Comparison of Experimental to Theoretical Pipe Strains During Water Hammer

2006 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Hoop Stress ◽  
Maximum Stress ◽  
Pipe Wall ◽  
Equations Of Motion ◽  
Water Hammer ◽  
Stress And Strain ◽  
Hoop Strain ◽  
Fluid Transient ◽  
Basic Equations ◽  
Experimental Strains

Experimental strains during water hammer were compared to theoretical equations for strain. These equations were derived from the basic equations of motion, which lead to equations for the hoop stress and hoop strain. In this particular case, a sudden pressure increase traveling in a pipe was measured, and the hoop strains resulting from this fluid transient were also measured. Measuring the strains at numerous locations along the pipe permitted comparison of the strains as a function of position with respect to the fluid shock wave. This comparison of strains at different positions along the pipe permits analysis of the vibratory nature of the strain in the pipe wall. Essentially, the equations of motion provide an approximate technique to find the maximum stress and strain due to water hammer.

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