II. The angular motion of a freely falling rocket

1964 ◽  
Vol 279 (1379) ◽  
pp. 523-533
Keyword(s):  
Angular Velocity ◽  
Unit Length ◽  
Free Fall ◽  
Axisymmetric Body ◽  
Rigid Bodies ◽  
Angular Motion ◽  
Time Interval ◽  
Angular Momentum Vector ◽  
Centre Of Mass ◽  
Aerodynamic Forces

The motion of a rocket with its propellant exhausted and above the heights where aerodynamic forces can be used to control its motion, can be considered as that of a rigid body in free flight, subjected to small perturbations by weak aerodynamic forces. This permits the separate consideration of the motion of the centre of mass of the rocket along an approximately ‘free fall’ trajectory and the rotation of the rocket about its centre of mass. The rotational motion of free rigid bodies is well known and may be readily visualized by means of Poinsot’s construction (Corben & Stehle 1960). This analysis may be applied to the motion of a rocket with an accuracy which depends on the smallness of the residual aerodynamic forces and the time interval over which the ‘free fall’ approximation is applied. The Skylark rocket vehicle is a long axisymmetric body of approximately uniform mass per unit length. The momental ellipsoid of such a body is a long ellipsoid of revolution with its major axis along the spin axis of the rocket. In this case, the angular motion will consist only of roll and regular precession. In the early stages of the flight the rocket is given some spin motion by aero­dynamic forces on the fins. The angle between the geometrical axis of the rocket and the angular momentum vector is small and can change only slowly because of the aerodynamic forces which are important during the initial stages of the flight. The rate of precession of the rocket axis is much smaller than the rate of spin. In these circumstances, the angular motion will be as shown in figure 11 and can be regarded as roll about the vehicle axis OV with angular velocity ω and precession of this axis about an invariant direction OC with angular velocity Ω. The semi-angle, COV = ρ , of the precession cone is given by cos p = I L / I T ω / Ω , where I L and I T are the moments of inertia about longitudinal and transverse axes passing through the centre of mass.

ESTIMATION OF AERODYNAMIC FORCES AND MOMENTS DERIVATIVES WITH RESPECT TO THE ANGULAR VELOCITY COMPONENTS OF THE AIRCRAFT MODEL IN A WIDE RANGE OF ANGLES OF ATTACK

2018 ◽  
Vol 49 (1) ◽  
pp. 43-64
Author(s):  
Mikhail Alekseyevich Golovkin ◽  
Andrey Aleksandrovich Efremov ◽  
Miroslav Sergeevich Makhnev
Keyword(s):  
Angular Velocity ◽  
Aerodynamic Forces ◽  
Aircraft Model ◽  
Wide Range

scholarly journals SEDIGISM: the kinematics of ATLASGAL filaments

2018 ◽  
Vol 619 ◽  
pp. A166 ◽  
Author(s):  
M. Mattern ◽  
J. Kauffmann ◽  
T. Csengeri ◽  
J. S. Urquhart ◽  
S. Leurini ◽  
...  
Keyword(s):  
Unit Length ◽  
Dust Emission ◽  
Free Fall ◽  
Outer Radius ◽  
Line Of Sight ◽  
Fall Velocity ◽  
Automated Algorithm ◽  
Power Law Exponent ◽  
Continuum Data ◽  
Self Gravity

Analyzing the kinematics of filamentary molecular clouds is a crucial step toward understanding their role in the star formation process. Therefore, we study the kinematics of 283 filament candidates in the inner Galaxy, that were previously identified in the ATLASGAL dust continuum data. The 13CO(2 – 1) and C18O(2 – 1) data of the SEDIGISM survey (Structure, Excitation, and Dynamics of the Inner Galactic Inter Stellar Medium) allows us to analyze the kinematics of these targets and to determine their physical properties at a resolution of 30′′ and 0.25 km s−1. To do so, we developed an automated algorithm to identify all velocity components along the line-of-sight correlated with the ATLASGAL dust emission, and derive size, mass, and kinematic properties for all velocity components. We find two-third of the filament candidates are coherent structures in position-position-velocity space. The remaining candidates appear to be the result of a superposition of two or three filamentary structures along the line-of-sight. At the resolution of the data, on average the filaments are in agreement with Plummer-like radial density profiles with a power-law exponent of p ≈ 1.5 ± 0.5, indicating that they are typically embedded in a molecular cloud and do not have a well-defined outer radius. Also, we find a correlation between the observed mass per unit length and the velocity dispersion of the filament of m ∝ σv2. We show that this relation can be explained by a virial balance between self-gravity and pressure. Another possible explanation could be radial collapse of the filament, where we can exclude infall motions close to the free-fall velocity.

scholarly journals ρ-Libration point in the three body problem

2021 ◽  
Vol 57 (3) ◽  
pp. 330-346
Author(s):  
A. P. Ryabushko ◽  
T. A. Zhur
Keyword(s):  
Angular Velocity ◽  
General Theory ◽  
Libration Point ◽  
Homogeneous Medium ◽  
Libration Points ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Centre Of Mass ◽  
Newtonian Approximation ◽  
Two Bodies

Herein, the restricted circular three-body problem in homogeneous and inhomogeneous media is considered. Particular attention is paid to libration points. The conditions of their existence or non-existence in the Newtonian and post-Newtonian approximations of the general theory of relativity are derived. Several regularities, new Newtonian and relativistic effects arising due to the impact of the additional relativistic forces on bodies of gravitational fields of mediums in the differential equations of the motion of bodies are indicated. Using the previously derived equations of the motion of two bodies A1, A2 in the medium, the authors substantiated the following statements. In a homogeneous medium (density of the medium ρ = const) in the Newtonian approximation of the general theory of relativity there are ρ-libration points , 1,...,5, moving along the same circles as the Euler and Lagrangian libration points Li but with an angular velocity 0 , greater than the angular velocity ω0 of libration points Li in a vacuum. Bodies A1, A2 also move along their circles with an angular velocity 0 > w When passing from the Newtonian approximation of the general theory of relativity to the post-Newtonian approximation of the general theory of relativity, the centre of mass of two bodies, resting in a homogeneous medium in the Newtonian approximation of the general theory of relativity, must move along a cycloid. The trajectories of the bodies can not be circles, the libration points Li disappear. In the case of an inhomogeneous medium distributed, for example, spherically symmetrically, the centre of mass of two bodies, already in the Newtonian approximation of the general theory of relativity, must move along the cycloid, despite it was at rest in the void. Therefore, bodies A1, A2 must describe loops that form, figuratively speaking, a «lace», as in the case of a homogeneous medium in the post-Newtonian approximation of the general theory of relativity. The figure illustrating the situation is provided. Due to the existence of the «lace» effect, the libration point Li movements are destroyed. In the special case, when the masses of bodies A1, A2 are equal (m1 = m2), the cycloids disappear and all the ρ-libration points exist in homogeneous and inhomogeneous media in the Newtonian and post-Newtonian approximations of the general theory of relativity. Numerical estimates of the predicted patterns and effects in the Solar and other planetary systems, interstellar and intergalactic mediums are carried out. For example, displacements associated with these effects, such as the displacement of the centre of mass, can reach many billions of kilometres per revolution of the two-body system. The possible role of these regularities and effects in the theories of the evolution of planetary systems, galaxies, and their ensembles is discussed. A brief review of the studies carried out by the Belarusian scientific school on the problem of the motion of bodies in media in the general theory of relativity is given.

Measurement of the angular motion parameters of the mirror of the scanning device

2021 ◽  
pp. 3-7
Author(s):  
Petr A. Pavlov ◽  
Elena M. Ivashchenko
Keyword(s):  
Angular Velocity ◽  
Angular Position ◽  
Low Frequency ◽  
Frequency Region ◽  
Angular Motion ◽  
Main Attention ◽  
Scanning Angle ◽  
Scanning Device ◽  
Environmental Monitoring System

A scanning device for a space-based environmental monitoring system has been investigated. The main attention is paid to the study of the parameters of the angular motion of the mirror of the scanning device, the uniformity of rotation of which largely determines the quality of the image of the Earth's surface. The principle and results of measuring the parameters of the mirror rotation carried out in a wide angular range are considered. The measurements were performed using a dynamic goniometer-autocollimator, which has been calibrated at the State Standard of Plane Angle Unit GET 22-2014. The repeatability of the average angular velocity of the scanning device mirror and the repeatability of the initial scanning angle are calculated. Nonstationarity in mathematical expectation and variance in random deviations of the angular motion of the mirror from the linear law of scanning is noted. The use of wavelet analysis revealed the frequency of excitation of oscillations in the low-frequency region of the spectrum. The possibility of using the a dynamic goniometer-autocollimator for measuring not only the angular position of the scanning device mirror, but also the angular velocity is shown.

THE CALIBRATION OF AN ARRAY OF ACCELEROMETERS

2011 ◽  
Vol 35 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Dany Dubé ◽  
Philippe Cardou
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Least Squares ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Rigid Bodies ◽  
New Method ◽  
Scale Factors ◽  
Array Calibration ◽  
The One

An accelerometer-array calibration method is proposed in this paper by which we estimate not only the accelerometer offsets and scale factors, but also their sensitive directions and positions on a rigid body. These latter parameters are computed from the classical equations that describe the kinematics of rigid bodies, and by measuring the accelerometer-array displacements using a magnetic sensor. Unlike calibration schemes that were reported before, the one proposed here guarantees that the estimated accelerometer-array parameters are globally optimum in the least-squares sense. The calibration procedure is tested on OCTA, a rigid body equipped with six biaxial accelerometers. It is demonstrated that the new method significantly reduces the errors when computing the angular velocity of a rigid body from the accelerometer measurements.

scholarly journals Solving a Problem of Rotary Motion for a Heavy Solid Using the Large Parameter Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Small Parameter ◽  
Initial Conditions ◽  
Geometric Interpretation ◽  
Rigid Bodies ◽  
Parameter Method ◽  
Large Parameter ◽  
Small Parameter Method ◽  
Rotational Motions ◽  
The Stability

The small parameter method was applied for solving many rotational motions of heavy solids, rigid bodies, and gyroscopes for different problems which classify them according to certain initial conditions on moments of inertia and initial angular velocity components. For achieving the small parameter method, the authors have assumed that the initial angular velocity is sufficiently large. In this work, it is assumed that the initial angular velocity is sufficiently small to achieve the large parameter instead of the small one. In this manner, a lot of energy used for making the motion initially is saved. The obtained analytical periodic solutions are represented graphically using a computer program to show the geometric periodicity of the obtained solutions in some interval of time. In the end, the geometric interpretation of the stability of a motion is given.

Nonaxisymmetric Acoustic Radiation and Scattering From Rigid Bodies of Revolution Using the Surface Variational Principle

1998 ◽  
Vol 120 (1) ◽  
pp. 95-103 ◽  
Author(s):  
J. H. Ginsberg ◽  
Kuangcheng Wu
Keyword(s):  
Variational Principle ◽  
Rigid Body ◽  
Acoustic Radiation ◽  
Axisymmetric Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Convergence Properties ◽  
Bodies Of Revolution ◽  
Computer Codes ◽  
Acoustic Fluid

The surface variational principle (SVP), which represents the surface response as a series of basis functions spanning the entire surface, provides a global description of acoustic fluid-structure interaction that has many of the benefits associated with analytical methods. This paper describes the extension of SVP to model the interaction between the velocity and pressure on the surface of an axisymmetric body subjected to nonaxisymmetric excitation. Problems addressed are radiation due to arbitrary rigid body motion, and scattering associated with arbitrary incidence of a plane wave on a stationary rigid body. Numerical results are presented for flat-ended and hemi-capped cylinders. These results are compared to those obtained from the CHIEF-88 and SHIP-92 computer codes. The convergence properties of SVP are examined in detail, particularly for its requirements when ka is in the upper part of the mid-frequency range.

Numerical Analysis of Impact Loads on Subsea Structures During Water Entry in Presence of Waves

2020 ◽  
Author(s):  
Gustavo Garcia Momm ◽  
Ivan Fábio Mota de Menezes
Keyword(s):  
Constant Velocity ◽  
Oil And Gas ◽  
Free Fall ◽  
Water Entry ◽  
Gas Production ◽  
Rigid Bodies ◽  
Bottom Surface ◽  
Impact Loads ◽  
Flat Bottom ◽  
The Impact

Abstract Subsea structures employed on offshore oil and gas production systems are likely to be subject to severe loads during deployment. Lowering these structures through the wave zone is a critical operation and the prediction of the loads associated is complex as it involves accelerations of these bodies induced by the vessel motion and the sea surface displacements. This work presents a numerical approach to assessment of the effect of waves on the impact loads that subsea structures are subject to during water entry. A 2D one degree of freedom model using the SPH method was developed to estimate slamming loads on rigid bodies during water entry considering both calm and wavy surfaces. Initially the model was employed to simulate the water entry of wedge considering both free fall and constant velocity cases, obtaining loads profile similar to experiments and numerical simulations from the literature. Later, the constant velocity model was configured to a flat bottom surface rigid body in order to represent a subsea manifold. A regular waves generator provided different wavelength, height and phase enabling slamming load assessment in various situations.

The Generation of Contact Surfaces of Indexing Cam Mechanisms: A Unified Approach

1990 ◽  
Author(s):  
M. A. Gonzalez-Palacios ◽  
J. Angeles ◽  
Ch. Cai
Keyword(s):  
Angular Velocity ◽  
Velocity Ratio ◽  
Rigid Bodies ◽  
Ruled Surfaces ◽  
Time Varying ◽  
Unified Approach ◽  
Unified Framework ◽  
Spatial Mechanisms ◽  
Contact Surfaces

Abstract In this paper the ruled surfaces of two rigid bodies that are in contact while moving with a prescribed time-varying angular-velocity ratio are generated. These are then used as the contact surfaces of indexing cam mechanisms. In this way, planar, spherical and spatial mechanisms can be synthesized in a unified framework. The approach is illustrated with various examples.

Dynamics of an axisymmetric body spinning on a horizontal surface. II. Self-induced jumping

2005 ◽  
Vol 461 (2058) ◽  
pp. 1753-1774 ◽  
Author(s):  
Y Shimomura ◽  
M Branicki ◽  
H.K Moffatt
Keyword(s):  
Dynamical System ◽  
Exact Solution ◽  
High Frequency ◽  
Multiple Scale ◽  
Frequency Component ◽  
Axisymmetric Body ◽  
High Frequency Component ◽  
Centre Of Mass ◽  
Normal Reaction ◽  
Loss Of Contact

Following part I of this series, the general spinning motion of an axisymmetric rigid body on a horizontal table is further analysed, allowing for slip and friction at the point of contact. Attention is focused on the case of spheroids whose density distribution is such that the centre-of-mass and centre-of-volume coincide. The governing dynamical system is treated by a multiple-scale technique in order to resolve the two time-scales intrinsic to the dynamics. An approximate solution for the high-frequency component of the motion reveals that the normal reaction can oscillate with growing amplitude, and in some circumstances will fall to zero, leading to temporary loss of contact between the spheroid and the table. The exact solution for the free motion that ensues after this ‘jumping’ is analysed, and the time-dependence of the gap between the spheroid and the table is obtained up to the time when contact with the table is re-established. The analytical results agree well with numerical simulations of the exact equations, both up to and after loss of contact.

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